Когомології напівгруп: Автореф. дис… д-ра фіз.-мат. наук / Б.В. Новіков, Київ. ун-т ім. Т.Шевченка. — К., 1999. — 33 с. — укp.

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Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea

IIA?EIA Ai?en Aieiaeeie?iae/

OAeE 512.664.4

EIAIIIEIA?? IAI?AA?OI

01.01.06 – aeaaa?a ? oai??y /enae

AAOI?AOA?AO

aeena?oaoe?? ia caeiaoooy iaoeiaiai nooiaiy

aeieoi?a o?ceei-iaoaiaoe/ieo iaoe

Ee?a-1999

Aeena?oaoe??th ? ?oeiien

?iaioa aeeiiaia a Oa?e?anueeiio aea?aeaaiiio oi?aa?neoao?

Io?oe?ei? iiiiaioe: aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

I?OAEUeIA Ieaenaiae? Aaneeueiae/, i?ioani?, i?i?aeoi?, Iineianueeee
aea?aeaaiee oi?aa?neoao

?i. I. A. Eiiiiiniaa, i. Iineaa

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

III?CIANUeEEE ?ineo Nieiiiiiae/, i?ioani? eaoaae?e aeui? iaoaiaoeee,
?in?enueeee aea?aeaaiee a?ae?iiaoai?ieia?/iee oi?aa?neoao, i.
Naieo-Iaoa?ao?a

aeieoi? o?ceei-iaoaiaoe/ieo iaoe,

I?IOANIA ?ai? Aieiaeeie?iae/, i?ioani? eaoaae?e aeine?aeaeaiiy
iia?aoe?e, Ee?anueeee oi?aa?neoao ?iai? Oa?ana Oaa/aiea, i. Ee?a

I?ia?aeia onoaiiaa: Euea?anueeee aea?aeaaiee oi?aa?neoao ?i. ?. O?aiea,

i. Euea?a

Caoeno a?aeaoaeaoueny 30.08.1999 ?. i 14-00 aiaeei? ia can?aeaii?
niaoe?ae?ciaaii? a/aii? ?aaee Ae 26.001.18 i?e Ee?anueeiio oi?aa?neoao?
?iai? Oa?ana Oaa/aiea ca aae?anith 252127, i. Ee?a-127, i?iniaeo aeaae.
Aeooeiaa, 6, Ee?anueeee oi?aa?neoao ?i. O.Oaa/aiea,
iaoai?ei-iaoaiaoe/iee oaeoeueoao.

C aeena?oaoe??th iiaeia iciaeiieoenue o iaoeia?e a?ae?ioaoe?
oi?aa?neoaoo ca aae?anith: i. Ee?a, aoe. Aieiaeeie?nueea, 58.

Aaoi?aoa?ao ?ic?neaiee 14.07.1999 ?.

A/aiee nae?aoa?

niaoe?ae?ciaaii? a/aii? ?aaee EE?E*AIEI A.A.

CAAAEUeIA OA?AEOA?ENOEEA ?IAIOE

Aeooaeuei?noue oaie. Iaoiaee aiiieia?/ii? aeaaa?e i?ioyaii iaeaea
i?anoi??//y oni?oii aeei?enoiaothoueny aeey ?ica’ycaiiy caaea/ o
??ciiiai?oieo ?icae?eao iaoaiaoeee. Eeane/iei i?eeeaaeii ? aeei?enoaiiy
eiaiiieia?e ooiaeaiaioaeueieo a?oi oiiieia?/ieo i?inoi??a a aeaaa?a?/i?e
oiiieia??. Iaiao?aeii a?aecia/eoe oaeiae i?iia?nuee? ?iaioe

Ae. E. Oaaeae??aa ii iiaoaeia? eiaiiieia?e a?oi ye aia?aoa aeey
aeine?aeaeaiiy iioe?aiue a?oi.

C eiaiiieia?yie iai?aa?oi ni?aaa ianoi?oue ?iaeoa. Oi/a aiie
?icaeyaeaeeny aaea A. Ea?oaiii ? N. Aeeaiaa?aii o “Aiiieia?/i?e aeaaa??
” (? iaa?oue ?ai?oa – o noaooyo N. Aeeaiaa?aa ? N. Iaeeaeia 1945 – 51
??.), aea aiie ia caeo/aee aei naaa na?eicii? oaaae aeaaa?a?no?a. Oea
aeeeeeaii a ia?oo /a?ao oei, ui o?aea?ia? iioe?aiiy, iia’ycai? c 2- ?
3-aei??ieie eiaiiieia?yie Aeeaiaa?aa – Iaeeaeia (iaaeae? ie aoaeaii
iaceaaoe ?o AI-eiaiiieia?yie), ia a?athoue oaei? ?ie? i?e aeine?aeaeaii?
iiaoaeiae iai?aa?oi, ye o oai??? a?oi. I?ci?oa c’yaeany ?yae ?ia?o ([15
– 17] oa ?i.), o yeeo ii ??ciiiai?oieo (iao?aea?iaeo) oeiao iioe?aiue
iiaoaeiaaii iia? eiino?oeoe?? eiaiiieia?e iai?aa?oi. Noaei ynii, ui
canoinoaaiiy aiiieia?/ieo iaoiae?a o oai??? iai?aa?oi ia ae/a?io?oueny
AI-eiaiiieia?yie.

I?ioa aeine?aeaeaiiy AI-eiaiiieia?e iai?aa?oi i?iaeiaaeoaaeiny. Ia?oith
ooiaeaiaioaeueiith ?iaioith a oeueiio iai?yieo iiaeia aaaaeaoe noaooth
O. Ieei [19], o ye?e aea/aeeny eiaiiieia?? ??ciiiai?oieo oei?a
iai?aa?oi, ui iathoue yae?i Nooeaae/a (iaeiaioee aeaia?/iee ?aeaae), ?,
cie?aia, iienaii eiaiiieia?? oe?eeii i?inoeo iai?aa?oi (a?aecia/eii, ui
a oe?e ?iaio? c?iaeaii oaeiae ni?iao ca’ycaoe eiaiiieia?/io aei??i?noue
?c iiiyooyi neeaaeiino? iai?aa?oie, aaaaeaiei ?ioaenii ? ?i.).

Iaei cia/aiiy ? ?iaioa A. I?o/aeea [18], o ye?e, cie?aia, aea/aeany
eiaiiieia?/ia aei??i?noue iai?aa?oi. I?o/aee aeia?a, ui oae caaia
/anoeiai naiaiaeia iai?aa?oia (naiaiaeiee oa?? naiaiaeii? a?oie ?
naiaiaeii? iai?aa?oie) ia? eiaiiieia?/io aei??i?noue, yea aei??aith? 1,
? i?eionoea ii aiaeia?? c a?aeiiith oai?aiith Noiee?iana-Noiia, ui a??ii
e cai?ioia. I?ioa, aeena?oaioii o 1982 ?. aoa iioae?eiaaiee
eiio?i?eeeaae aei a?iioace I?o/aeea, ? oaeei /eiii, ieoaiiy i?i
aeanoeaino? iai?aa?oi aei??iino? 1 caeeoeeiny a?aee?eoei. Iaaeae? ?yae
aeaaa?a?no?a [10, 20] ?icaeyaeaa ieoaiiy i?i eiaiiieia?/io aei??i?noue
aeayeeo ??ciiaeae?a iai?aa?oi.

Ua iaeia iaeeane/ia eiino?oeoe?y eiaiiieia?e c’yaeeany a ?acoeueoao?
aea/aiiy i?iaeoeaieo cia?aaeaiue iai?aa?oi [7]. I?e oeueiio
ioeueoeie?eaoi? Oo?a yaey?oueny ia a?oiith, a eiiooaoeaiith ?iaa?niith
iai?aa?oiith. Inoaiiy ?, ye a?aeiii, iai?ano?oeoo?ith a?oi, yea, o naith
/a?ao, iieno?oueny ca aeiiiiiaith niaoe?aeueii? eiino?oeoe?? oae caaieo
0-eiaiiieia?e. Ie?aiee aeiaaeie 0-eiaiiieia?e (eiee ae?y iai?aa?oie ia
iiaeoe? o?ea?aeueia), aoa ?icaeyiooee O. Eea?eii [11] i?e aea/aii?
aoaeiae aeayeeo iao?e/ieo aeaaa?.

I?ci?oa aeena?oaioii aoei iieacaii, ui 0-eiaiiieia?? yaeythoueny
ei?enieie ? aeey ia/eneaiiy AI-eiaiiieia?e iai?aa?oi; naia c ?oiueith
aeiiiiiaith aoa iiaoaeiaaiee aeuacaaaeaiee eiio?i?eeeaae aei a?iioace
I?o/aeea.

Ia?aoo? a?aecia/eii na??th ?ia?o Oaeea, Ea?niia ? No?aeea?a [12 –14,
21], o yeeo iiaoaeiaaii oae caaiee iiii?ae A?aoa?a, ui iieno? eean
neeueii i?eia?ieo anioe?aoeaieo aeaaa? iiae?aii oiio, ye a?oia A?aoa?a
eeaneo?eo? oeaio?aeuei? i?ino? aeaaa?e. O aeena?oaoe?? iieacaii, ui
aea/aiiy iiii?aea A?aoa?a oaae caiaeeoueny aei 0-eiaiiieia?e.

Iaaaaeaiee aeua ei?ioeee iaeyae iieaco?, ui ca?ac eiaiiieia?? iai?aa?oi
ia o?eueee i?aaenoaaeythoue naiino?eiee ?ioa?an, aea ? ciaoiaeyoue
canoinoaaiiy a ?ioeo ?icae?eao aeaaa?e. Oei a?eueo aeooaeueiei noa?
ieoaiiy i?i ?ic?iaeo iaoiae?a ?oiueiai ia/eneaiiy. Oeueiio iai?yieo
i?enay/aii cia/io /anoeio aeena?oaoe??. E??i oiai, o i?e aeeeaaeathoueny
?acoeueoaoe canoinoaaiiy 0-eiaiiieia?e aei aea/aiiy aeanoeainoae
iiii?aea A?aoa?a ? aeine?aeaeothoueny iai?aa?oie eiaiiieia?/iie
aei??iino? 1.

O aeena?oaoe?? ia?aaaaeii aeei?enoiaothoueny iaoiaee aiiieia?/ii?
aeaaa?e, oai??? eaoaai??e ? oai??? iai?aa?oi.

Ca’ycie ?c iaoeiaeie i?ia?aiaie ? oaiaie. ?iaioo aeeiiaii ia eaoaae??
oai??? ooieoe?e ? ooieoe?iiaeueiiai aiae?co iaoai?ei-iaoaiaoe/iiai
oaeoeueoaoo Oa?e?anueeiai aea?aeaaiiai oi?aa?neoaoo.Aeine?aeaeaiiy, ye?
eaaee a iniiao aeaii? aeena?oaoe?eii? ?iaioe, i?iaiaeeeeny a?aeiia?aeii
aei

1) IAe? “Aeine?aeaeaiiy a oai??? iai?aa?oi ? noi?aeieo aaeocyo
iaoaiaoeee” (1994-95 ??., iiia? ?a?no?aoe?? 0194U012799);

2) IAe? “Aeine?aeaeaiiy c oai??? iai?aa?oi ? aiiieia?/ii? aeaaa?e”

(1996-97 ??., iiia? ?a?no?aoe?? 0197U009308).

Iaoith aeena?oaoe?? ?:

a) canoinoaaiiy 0-eiaiiieia?e aei aeine?aeaeaiiy aeanoeainoae iiii?aea
A?aoa?a;

a) iiaoaeiaa oai??? /anoeiaeo eiaiiieia?e iai?aa?oi ? aeei?enoaiiy ?o
aei ia/eneaiiy AI-eiaiiieia?e;

a) aea/aiiy aeanoeainoae eiaiiieia?/iie aei??iino? iai?aa?oi (a ia?oo
/a?ao, iai?aa?oi ?c nei?i/aiiyi).

Iaoeiaa iiaecia, oai?aoe/ia ? i?aeoe/ia oe?ii?noue. Aaaaeaii iiiyooy
iiaeeo?eaoe?? a?oie, ca aeiiiiiaith yeiai io?eiaii iia? aeanoeaino?
iiii?aea A?aoa?a.

Cai?iiiiiaaii iiao eiino?oeoe?th /anoeiaeo eiaiiieia?e iai?aa?oi,
aea/aii ?oi? aeanoeaino? (o oiio /ene? eio?i?/ia cia?aaeaiiy ? ca’ycie
?c AI-eiaiiieia?yie). C ?oiueith aeiiiiiaith ciaeaeaii a?oie
AI-eiaiiieia?e aeayeeo eean?a iai?aa?oi ?, cie?aia, iaaaaeaii na??th
eiio?i?eeeaae?a aei a?iioace I?o/aeea.

Aeiaaaeaii, ui iai?aa?oie ?c nei?i/aiiyi eiaiiieia?/ii? aei??iino? 1
aeeaaeathoueny aei naiaiaeii? a?oie. O eiiooaoeaiiio aeiaaeeo aeey oaeeo
iai?aa?oi io?eiaii iiaia iienaiiy.

An? iaea?aeai? a aeena?oaoe?ei?e ?iaio? ?acoeueoaoe ? iiaeie.

I?aeoe/ia cia/aiiy io?eiaieo ?acoeueoao?a. ?acoeueoaoe ? iaoiaee
aeena?oaoe?? iiaeooue aooe canoiniaai? a oai??? anioe?aoeaieo aeaaa?
(aeey eeaneo?eaoe?? aeaaa? ca aeiiiiiaith /anoeiaeo eiaiiieia?e), aeey
aea/aiiy iai?aa?oi ? ?ioeo aeaaa?a?/ieo nenoai iaei? eiaiiieia?/iie
aei??iino?, aeey aeyaeaiiy ca’yce?a i?ae oai???th iai?aa?oi ?
aeaaa?a?/iith oiiieia??th. Aiie oaeiae iiaeooue aooe aeei?enoai? a
iaa/aeueiiio i?ioean? i?e /eoaii? eaeoe?e ii niaoe?aeueiei eo?nai
“Aiiieia?/ia aeaaa?a”, “Oai?ey iai?aa?oi” ? “Eiaiiieia?? a?oi ?
iai?aa?oi” ia iaoai?ei-iaoaiaoe/ieo ? o?ceei-iaoaiaoe/ieo oaeoeueoaoao
aeueo iaa/aeueieo caeeaae?a Oe?a?ie III ? IV ??aiy ae?aaeeoaoe??.

Iniaenoee aianie caeiaoaa/a. On? iaae?oeiaai? ?iaioe c oaie aeena?oaoe??
aeeiiaii aac ni?aaaoi??a, ca aeiyoeii [36] ? [40] (ni?aaaoi?e – I. N.
Eau??aa ? E. Ei?aeaeaa).

O iaio noaooyo aeena?oaioo iaeaaeaoue iinoaiiaee caaea/, a oaeiae
aeiaaaeaiiy oai?ai 1.1, 1.2 o [36] ? aeiaaaeaiiy on?o oai?ai o [40].

Ia caoeno aeiinyony ianooii? iniiai? iieiaeaiiy:

1. Aea/aiiy ca aeiiiiiaith /anoeiaeo eiaiiieia?e aeanoeainoae iiii?aea
A?aoa?a; iien aeayeeo oei?a iiaeeo?eaoe?e a?oi.

2. Iiaoaeiaa ? aeanoeaino? /anoeiaeo eiaiiieia?e iai?aa?oi; canoinoaaiiy
aei ia/eneaiiy eeane/ieo a?oi eiaiiieia?e.

3. Aeine?aeaeaiiy ??ciiiai?oieo eean?a iai?aa?oi eiaiiieia?/ii?
aei??iino? 1.

On? ?acoeueoaoe aeena?oaoe?? yaeythoueny iaoaiaoe/ieie oai?aiaie,
aeiaaaeaieie ia i?eeiyoiio a no/anii? iaoaiaoeoe? ??ai? no?iaino?.

Ai?iaaoe?y ?acoeueoao?a aeena?oaoe??. Iniiai? ?acoeueoaoe
aeena?oaoe?eii? ?iaioe aeiiia?aeaeeny ia oaeeo eiioa?aioe?yo,
neiiic?oiao ? nai?ia?ao:

XVI Ananithcia aeaaa?a?/ia eiioa?aioe?y – Eai?ia?aae, 1981;

XVII Ananithcia aeaaa?a?/ia eiioa?aioe?y – I?inuee, 1983;

XVIII Ananithcia aeaaa?a?/ia eiioa?aioe?y – Eeoei?a, 1985;

XIX Ananithcia aeaaa?a?/ia eiioa?aioe?y – Euea?a, 1987;

X Ananithciee neiiic?oi c oai??? a?oi – I?inuee, 1986;

III Ananithciee neiiic?oi c oai??? iai?aa?oi – Naa?aeeianuee, 1988;

?icoe?aiee aeaaa?a?/iee nai?ia? Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana
Oaa/aiea, i?enay/aiee 100-??//th c aeiy ia?iaeaeaiiy aeaaeai?ea I. TH.
Oi?aeoa – Ee?a, 1991;

?icoe?aiee aeaaa?a?/iee nai?ia? Ee?anueeiai oi?aa?neoaoo ?iai? Oa?ana
Oaa/aiea, i?enay/aiee 80-??//th ooiaeaoi?a eaoaae?e aeaaa?e ?
iaoaiaoe/ii? eia?ee i?io. E. A. Eaeoaei?ia – Ee?a, 1994;

I?aeia?iaeiee eieiea?oi c iai?aa?oi – Naaaae, Oai?ueia, 1994;

I?aeia?iaeia eiioa?aioe?y c aeaaa?e, eia?ee ? aeene?aoii? iaoaiaoeee –
I?o, THaineaa?y, 1995;

Ae?oaee ?a?iiaenueeee iaoaiaoe/iee eiia?an – Aoaeaiaoo, Oai?ueia, 1996;

I?aeia?iaeia eiioa?aioe?y c oai??? cia?aaeaiue ? eiii’thoa?ii? aeaaa?e a
Ee?anueeiio oi?aa?neoao? ?iai? Oa?ana Oaa/aiea – Ee?a, 1996;

I?aeia?iaeia aeaaa?a?/ia eiioa?aioe?y, i?enay/aia iai’yo? i?io.

E. I. Aeoneeia – Neia’yinuee, 1997.

Oace aeiiia?aeae iaae?oeiaaii a [41 – 47].

Ioae?eaoe??. Iniiai? ?acoeueoaoe aeena?oaoe?? iioae?eiaaii a 25
?iaioao, c ieo – 18 noaoae [22 – 40] , o oiio /ene? 2 noaoo? ?c
ni?aaaoi?aie ([36] ? [40]).

No?oeoo?a e ianya aeena?oaoe??. Aeena?oaoe?y neeaaea?oueny c anooio,
ie?aiiai ?icae?eo “Iicia/aiey ? aecia/aiiy”, i’yoe aeaa ? nieneo
e?oa?aoo?e.

Aeieeaaei?oa:

aeaaa 1 “0-Eiaiiieia?? ? iiii?ae A?aoa?a” i?noeoue 5 ?icae?e?a;aeaaa 2
“*anoeia? eiaiiieia??” i?noeoue 7 ?icae?e?a;aeaaa 3 “Iai?aa?oie
eiaiiieia?/ii? aei??iino? 1” i?noeoue 4 ?icae?ee;aeaaa 4 “Eiaiiieia?? oa
?aoeaeoeai? i?aeeaoaai???” i?noeoue 5 ?icae?e?a;

aeaaa 5 “Caaaeueia oai??y eiaiiieia?e iai?aa?oi” i?noeoue 4 ?icae?ee.

Caaaeueiee ianya aeena?oaoe?eii? ?iaioe neeaaea? 281 noi?. Nienie
e?oa?aoo?e i?noeoue 122 iaeiaioaaiiy.

CI?NO ?IAIOE

Eiaeia aeaaa ii/eia?oueny c ioeueiaiai ?icae?eo “Iiia?aaei? a?aeiiino?”,
ui i?noeoue aeiaeaoeiao ?ioi?iaoe?th, iaiao?aeio aeey /eoaiiy ianooiieo
?icae?e?a oe??? aeaae.

Iaaaaea?ii nii/aoeo iaeia c aecia/aiue AI-eiaiiieia?e iai?aa?oie.

Iaoae S – aeia?eueia iai?aa?oia, A – aoaeue-yeee S-iiaeoeue (iaaeae? ie
?icaeyaea?ii o?eueee e?a? iiaeoe?). *a?ac Cn(S, A) iicia/a?ony a?oia
an?o n-i?noeaaeo a?aeia?aaeaiue

f: S SYMBOL 180 \f “Symbol” \s 14 ? SYMBOL 188 \f “Symbol” \s 14 1/4
SYMBOL 180 \f “Symbol” \s 14 ? S SYMBOL 174 \f “Symbol” \s 14 ® A

(a?oia n-aei??ieo eieaioetha?a); eia?aie/iee iia?aoi?

SYMBOL 182 \f “Symbol” \s 14 ¶ n : Cn(S, A) SYMBOL 174 \f “Symbol” \s
14 ® Cn+1(S, A)

caaea?oueny ianooiiei /eiii:

SYMBOL 182 \f “Symbol” \s 14 ¶ n f(x1, …, xn+1) = x1f(x2, …, xn+1)
+

Oiae? SYMBOL 182 \f “Symbol” \s 14 ¶ n SYMBOL 182 \f “Symbol” \s 14 ¶
n-1 = 0, oiaoi Im SYMBOL 182 \f “Symbol” \s 14 ¶ n-1 = Bn(S, A) (a?oia
n-aei??ieo eia?aieoeue) SYMBOL 205 \f “Symbol” \s 14 I Eer SYMBOL
182 \f “Symbol” \s 14 ¶ n = Zn(S, A) (a?oia n-aei??ieo eioeeee?a) ?
a?oie EM-eiaiiieia?e aecia/athoueny ye

Hn(S, A) = Zn(S, A) / Bn(S, A).

Aeaao 1 i?enay/aii canoinoaaiith aia?aoo 0-eiaiiieiaee, ?ic?iaeaiiai
aaoi?ii ?ai?oa [6]. O ?icae?e? 1.1 iaaiaeyoueny iaiao?aei? a?aeiiino?
i?i 0-eiaiiieia?? oa oai?aoeei-eaoaai?ia ?ioai?aoaoe?y iaea?aeaieo
eiino?oeoe?e.

Aeey aeia?eueii? iai?aa?oie S c ioeai 0-iiaeoeai iaae S iaceaa?oueny
aaaeaaa (aaeeoeaia) a?oia A, aeey ye?e aecia/aii iiiaeaiiy

S \ 0 SYMBOL 180 \f “Symbol” \s 14 ? A SYMBOL 174 \f “Symbol” \s 14 ®
A,

ui caaeiaieueiy? aeey an?o s, t SYMBOL 206 \f “Symbol” \s 14 I S \ 0,
a,b SYMBOL 206 \f “Symbol” \s 14 I A oaeei oiiaai:

s(a + b)=sa + sb,

st SYMBOL 185 \f “Symbol” \s 14 ? 0 SYMBOL 219 \f “Symbol” \s 14 U
s(ta)=(st)a.

n-Aei??iei 0-eieaioethaii caaoueny /anoeiaa n-i?noeaaa a?aeia?aaeaiiy ?c
S a A, aecia/aia ia an?o oaeeo iaai?ao (s1, SYMBOL 188 \f “Symbol” \s 14
1/4 , sn), ui

a?aeiia?aeii.

Iniiaiei o oe??? aeaa? ? ?icae?e 1.2, aea iaaaaeaii canoinoaaiiy
0-eiaiiieia?e aei aeine?aeaeaiiy iiii?aea A?aoa?a, aecia/aiiai a na???
?ia?o Oaeea, Ea?niia ? No?aeea?a [12 – 14, 21] aeey eeaneo?eaoe??
neeueii i?eia?ieo anioe?aoeaieo aeaaa?.

Aeey aecia/aiiy oeueiai eeano aeaaa? cao?eno?ii iniiaia iiea K ? aoaeaii
a iiaeaeueoiio ?icaeyaeaoe o?eueee ne?i/aiii aei??i? aeaaa?e iaae K.

Iaoae F/K – ne?i/aiia naia?aaaeueia iioe?aiiy. Oeaio?aeueia i?inoa
F-aeaaa?a B caaoueny ii?iaeueiith iaae K, yeui eiaeia i?inoa eiiiiiaioa
(iai?ai?inoi?) aeaaa?e B SYMBOL 196 \f “Symbol” \s 14 Ae K Bop
?ciii?oia iiai?e iao?e/i?e aeaaa?? iaae oeaio?ii oe??? eiiiiiaioe.

I?ae i?i?iaeueiei oi/iei iiaeoeai ?icoi??oueny oi/iee iiaeoeue, ui ia
ia? aeanieo oi/ieo i?aeiiaeoe?a.

K-Aeaaa?a A caaoueny neeueii i?eia?iith iaae K, yeui aeey ia?
aeeiiothoueny ianooii? oiiae:

1) yeui J – ?aaeeeae aeaaa?e A, oi oaeoi?aeaaa?a A/J yaey?oueny
naia?aaaeueiith, i?inoith ? ii?iaeueiith iaae K;

2) yeui A = B SYMBOL 197 \f “Symbol” \s 14 A J – ?iceeaaeaiiy
Aaaeaea?aapia – Iaeueoeaaa (oaea ?nio? a neeo naia?aaaeueiino? A/J), oi
A yaey?oueny i?i?iaeueiei oi/iei B SYMBOL 196 \f “Symbol” \s 14 Ae K
Bop-iiaeoeai a?aeiinii ae?? (x SYMBOL 196 \f “Symbol” \s 14 Ae K
yop)a=xay aeey x, y SYMBOL 206 \f “Symbol” \s 14 I B, a SYMBOL 206 \f
“Symbol” \s 14 I A.

Iai?eeeaae, oeaio?aeuei? i?ino? aeaaa?e yaeythoueny neeueii i?eia?ieie.

Iaoae oaia?, ye ? aeua, L – ii?iaeueia iioe?aiiy iiey K, G – a?oia Aaeoa
oeueiai iioe?aiiy. Iicia/eii /a?ac P eean on?o neeueii i?eia?ieo iaae K
aeaaa? A = B SYMBOL 197 \f “Symbol” \s 14 A J, oaeeo, ui oeaio?
i?yiiai aeiaeaieo B ciaoiaeeoueny a L.

A ?iaio? Oaeea [13] iieacaii, ui ia P iiaeia oae aaanoe aeaeaaeaioi?noue
? aeiaooie ia eeanao oe??? aeaeaaeaioiino?, ui io?eia?ii iiii?ae, yeee
iicia/a?oueny M(G, L) ? caaoueny (a?aeiiniei) iiii?aeii A?aoa?a. Ie ia
aoaeaii iienoaaoe oeth aeaeaaeaioi?noue ? a?aeiia?aeiee aeiaooie, oiio
ui ?oi? aecia/aiiy caeiathoue aeineoue aaaaoi i?noey ? ia
aeei?enoiaothoueny iiaeae?. A?aecia/eii o?eueee, ui ia eean?
oeaio?aeueieo i?inoeo aeaaa? aiie caiaeyoueny aei a?aeiieo eiino?oeoe?e
aeey a?oie A?aoa?a e ui a [13] iiaoaeiaaii oaeiae ? aaniethoiee iiii?ae
A?aoa?a iiey K, yeee yaey?oueny ia’?aeiaiiyi iiii?ae?a aeaeyaeo M(G, L),
eiee L i?ia?aa? an? (ne?i/aii?) ii?iaeuei? iioe?aiiy iiey K.

Aeey ne?i/aiiiai ii?iaeueiiai iioe?aiiy L iiey K ?c a?oiith Aaeoa G
aecia/aiiy iiii?aea A?aoa?a M(G, L) a?ae??ciy?oueny a?ae aecia/aiiy
a?oie eiaiiieia?e Aaeoa H2(G, L) o?eueee oei, ui eioeeeee iiaeooue
i?eeiaoe ? ioeueia? cia/aiiy. A ?acoeueoao? oeueiai iiii?ae A?aoa?a M(G,
L) yaey?oueny (eiiooaoeaiith) ?iaa?niith iai?aa?oiith ?, oaeei /eiii,
iai?ano?oeoo?ith aaaeaaeo a?oi M SYMBOL 101 \f “Symbol” \s 14 e (G, L),
aea SYMBOL 101 \f “Symbol” \s 14 e i?ia?aa? iiiaeeio an?o
?aeaiiioaio?a iiii?aea M(G, L).

A?oie M SYMBOL 101 \f “Symbol” \s 14 e (G, L) aeiioneathoue iienaiiy o
oa?i?iao 0-eiaiiieia?e. Naia, o oaaeeoe? iiiaeaiiy iai?aa?oie G0 = G
SYMBOL 200 \f “Symbol” \s 14 E 0 (a?oia c ciai?oiuei i?e?aeiaiei ioeai)
c?o?aii ci?no aeayeeo ?? ee?oei ? aieoaii a ieo 0, oae, uia iiaa
iia?aoe?y aoea anioe?aoeaiith. Io?eiaia iai?aa?oia iaceaa?oueny
iiaeeo?eaoe??th a?oie G. Cie?aia, aecia/ath/e aeey aeaiiai ?aeaiiioaioo
SYMBOL 101 \f “Symbol” \s 14 e ia G SYMBOL 200 \f “Symbol” \s 14 E 0
iiao iia?aoe?th SYMBOL 183 \f “Symbol” \s 14 · :

ie iaea?aeo?ii iiaeeo?eaoe?th, ui iicia/a?ii /a?ac G SYMBOL 101 \f
“Symbol” \s 14 e .

sse iieacothoue ianooii? aea? i?iiiceoe??, iiii?ae A?aoa?a aecia/a?oueny
iiaeeo?eaoe?yie:

Eaia 1.2.1 ?nio? aca?iii iaeiicia/ia a?aeiia?aei?noue i?ae
?aeaiiioaioaie iiii?aea A?aoa?a M( G, L) ? iiaeeo?eaoe?yie a?oie G.

– ae?oaa a?oia 0-eiaiiieia?e iiii?aea G SYMBOL 101 \f “Symbol” \s 14 e
.

O [14, 21] aeey aea/aiiy iieono?oeoo?e ?aeaiiioaio?a iiii?aea A?aoa?a
aeei?enoiaothoueny aeaye? /anoeiai oii?yaeeiaai? iiiaeeie, iacaai?
“noao?aeoeaieie cieco /anoeiai oii?yaeeiaaieie G-i?a?oaie”.

A naia, iaoae, ye ? ?ai?o, G – ne?i/aiia a?oia, (Q, <) – /anoeiai oii?yaeeiaaia iiiaeeia c iaeiaioei aeaiaioii q ? caaeaii ae?thG SYMBOL 180 \f "Symbol" \s 14 ? Q SYMBOL 174 \f "Symbol" \s 14 ® Q : (g,x) SYMBOL 174 \f "Symbol" \s 14 ® g SYMBOL 42 \f "Symbol" \s 14 * x,oaeo, ui G SYMBOL 42 \f "Symbol" \s 14 * Q = Q. Iiiaeia Q caaoueny noao?aeoeaiith cieco /anoeiai oii?yaeeiaaiith G-i?aeoith, yeui aeey aoaeue-yeeo g, h SYMBOL 206 \f "Symbol" \s 14 I G, oaeeo, ui g SYMBOL 42 \f "Symbol" \s 14 * q < h SYMBOL 42 \f "Symbol" \s 14 * q, aeeiio?oueny oiiaaSYMBOL 34 \f "Symbol" \s 14 " f SYMBOL 206 \f "Symbol" \s 14 I G g SYMBOL 42 \f "Symbol" \s 14 * q < f SYMBOL 42 \f "Symbol" \s 14 * q < h SYMBOL 42 \f "Symbol" \s 14 * q SYMBOL 219 \f "Symbol" \s 14 U g-1f SYMBOL 42 \f "Symbol" \s 14 * q < g-1h SYMBOL 42 \f "Symbol" \s 14 * qO aeena?oaoe?? iieacaii, ui aeei?enoaiiy aeey oe??? iaoe iiaeeo?eaoe?e a?eueo ia?aaaaeii (aeea., iai?., iane?aeie 1.2.5).Iicia/eii /a?ac H i?aea?oio ia?aoeieo aeaiaio?a iiaeeo?eaoe?? G SYMBOL 101 \f "Symbol" \s 14 e . Aeeaaeaiiy H SYMBOL 200 \f "Symbol" \s 14 E 0 SYMBOL 174 \f "Symbol" \s 14 ® G SYMBOL 101 \f "Symbol" \s 14 e ?iaeoeo? aiiiii?o?ciO [14] i?e aeayeeo aeiaeaoeiaeo oiiaao anoaiiaeth?oueny ?i’?eoeai?noue a?aeia?aaeaiiy SYMBOL 106 \f "Symbol" \s 14 j . Ie ia/eneth?ii Ker SYMBOL 106 \f "Symbol" \s 14 j a ?io?e neooaoe??:Oai?aia 1.2.6. Iaoae iiaeeo?eaoe?y G SYMBOL 101 \f "Symbol" \s 14 e eiiiooaoeaia (?, ioaea, H, aoaeo/e i?aea?oiith oeaio?o a?oie G, ii?iaeueia). Iicia/eii /a?ac P i?aeiiea ia?ooiieo uiaei H aeaiaio?a c L. Oiae? ia? i?noea oi/ia iine?aeiai?noueCai?iiiiiaaia a aeena?oaoe?? iiiyooy iiaeeo?eaoe?? a?oie iiaea i?aaenoaaeyoe, iiaeeeai, ? naiino?eiee ?ioa?an. I?ioa iiaia iienaiiy iiaeeo?eaoe?e yaey?oueny aeineoue aaaeeith caaea/ath iaa?oue aeey i?inoi oeaooiaaieo a?oi, ui ?ethno?o?oueny a ?icae. 1.3 ia i?eeeaae? aeinniaeo iiaeeo?eaoe?e i?inoi? oeeee?/ii? a?oie.Iaoae G – aeia?eueia ne?i/aiia a?oia. Iacaaii ?? iiaeeo?eaoe?thS = G0( SYMBOL 42 \f "Symbol" \s 14 * )aeinniaith (ca aiaeia??th c a?aeiiith oiiaith Aeinna aeeaaeaiiy iai?aa?oie aei a?oie), yeuiSYMBOL 34 \f "Symbol" \s 14 " a,b SYMBOL 206 \f "Symbol" \s 14 I S (a SYMBOL 42 \f "Symbol" \s 14 * S) SYMBOL 199 \f "Symbol" \s 14 C (b SYMBOL 42 \f "Symbol" \s 14 * S) SYMBOL 185 \f "Symbol" \s 14 ? 0 SYMBOL 219 \f "Symbol" \s 14 U (a SYMBOL 206 \f "Symbol" \s 14 I b SYMBOL 42 \f "Symbol" \s 14 * S) SYMBOL 218 \f "Symbol" \s 14 U (b SYMBOL 206 \f "Symbol" \s 14 I a SYMBOL 42 \f "Symbol" \s 14 * S)Cacia/eii, ui aeey aeinniaeo iiaeeo?eaoe?e 0-eiaiiieia?? yaeythoueny o?ea?aeueieie:aeey aoaeue-yeiai 0-iiaeoey A.Iaaeae? iaoae G = SYMBOL 225 \f "Symbol" \s 14 a a | ap = 1 SYMBOL 241 \f "Symbol" \s 14 n yaey?oueny oeeee?/iith a?oiith i?inoiai ii?yaeeo p SYMBOL 179 \f "Symbol" \s 14 ? 3 c ii?iaeaeoth/ei aeaiaioii a, a S – ?? eiiooaoeaiith aeinniaith iiaeeo?eaoe??th, ui a?ae??ciy?oueny a?ae G0( SYMBOL 215 \f "Symbol" \s 14 * ) (oiaoi x SYMBOL 42 \f "Symbol" \s 14 * y = 0 aeey aeayeeo x, y SYMBOL 206 \f "Symbol" \s 14 I G).(n ?ac?a).Oai?aia 1.3.3. sseui eiiooaoeaia aeinniaa iiaeeo?eaoe?y S a?oie G, yaey?oueny 2-ii?iaeaeaiith, oiaea 1 SYMBOL 163 \f "Symbol" \s 14 F k SYMBOL 163 \f "Symbol" \s 14 F p-1, 2 SYMBOL 163 \f "Symbol" \s 14 F m SYMBOL 163 \f "Symbol" \s 14 F p-1.Iane?aeie 1.3.4. E?euee?noue an?o ??cieo (aea, iiaeeeai, ?ciii?oieo) eiiooaoeaieo 2-ii?iaeaeaieo aeinniaeo iiaeeo?eaoe?e a?oiu G aei??aith?(p-1)(p-2)/2.A aeiaaeeo, eiee iiaeeo?eaoe?y 3-ii?iaeaeaia, neooaoe?y aeyaey?oueny a?eueo neeaaeiith:Oai?aia 1.3.6. sseui eiiooaoeaia aeinniaa iiaeeo?eaoe?y S a?oie G, yaey?oueny 3-ii?iaeaeaiith, oi aeey a?aeiia?aeiei caniaii aea?aiiai ii?iaeaeoth/iai aeaiaioa aaea 2 SYMBOL 163 \f "Symbol" \s 14 F m SYMBOL 163 \f "Symbol" \s 14 F p-2.O ?icae?e? 1.4 iieacaii i?eeiie ia/eneaiiy 0-eiaiiieia?e iiaeeo?eaoe?e ia i?eeeaae? oeeee?/ii? a?oie i'yoiai ii?yaeeo.Iniiai? ?acoeueoaoe oe??? aeaae iioae?eiaaii a [23, 25, 32].Iiaeeea?noue i?eeeaaeaiiy 0-eiaiiieia?e aei ??ciiiai?oieo aeaaa?a?/ieo caaea/ (i?iaeoeai? cia?aaeaiiy iai?aa?oi, iao?e/i? aeaaa?e, iiii?aee A?aoa?a, ia/eneaiiy AI-eiaiiieia?e) i?eaiaeeoue aei iinoaiiaee ieoaiiy i?i ?o ocaaaeueiaiiy oeyoii ia?aoiaeo a?ae 0-eieaioetha?a aei aeia?eueieo (iane?eueee oea iiaeeeai) /anoeiaeo ooieoe?e ia iai?aa?oi?. Oaea aeine?aeaeaiiy i?iaiaeeoueny a aeaa? 2.Iaaaaea?ii aecia/aiiy ?aoeaeoeaii? i?aeeaoaai???.I?aeeaoaai?ey D eaoaai??? C caaoueny ?aoeaeoeaiith, yeui eiaeiiio ia'?eoo C SYMBOL 206 \f "Symbol" \s 14 I C c?noaaeaii ia'?eo RD(C) SYMBOL 206 \f "Symbol" \s 14 I D (yeee caaoueny D-?aoeaeoi?ii ia'?eoo C) ? ii?o?ciSYMBOL 101 \f "Symbol" \s 14 e D(C): C SYMBOL 174 \f "Symbol" \s 14 ® RD(C),oae?, ui aeey aoaeue-yeiai D SYMBOL 206 \f "Symbol" \s 14 I D ae?aa?aiaiaeiicia/ii aeiiiaith?oueny aei eiiooaoeaii? ii?o?ciii cHomD (RD(C), D).Ie aoaeaii oaeiae aeei?enoiaoaaoe a iaca? ?aoeaeoi?a i?eeiaoiee, ui a?aeiia?aea? ?iai? ?aoeaeoeaii? i?aeeaoaai???. Iai?eeeaae, yeui C – eaoaai??y iai?aa?oi, a D – i?aeeaoaai??y a?oi, oi D-?aoeaeoi? aoaeaii caaoe oaeiae a?oiiaei ?aoeaeoi?ii.Aeey iiaoaeiae /anoeiaeo eiaiiieia?e oa iiia?aaeiueiai aeyaeaiiy ?oi?o aeanoeainoae c?o/ii aeei?enoiaoaaoe iiaeoe? ia iaae iai?aa?oiaie, a iaae /anoeiaeie a?oii?aeaie. Iaoae X – aeayeee /anoeiaee a?oii?ae. (E?aei) X-iiaeoeai caaoueny aaeeoeaia aaaeaaa a?oia A, aeey yei? aecia/aii ae?thX SYMBOL 180 \f "Symbol" \s 14 ? A SYMBOL 174 \f "Symbol" \s 14 ® A,caaeiaieueiyth/o aeey on?o x, y SYMBOL 206 \f "Symbol" \s 14 I X, a, b SYMBOL 206 \f "Symbol" \s 14 I A oaeei oiiaai:x(a+b)=xa+xb,xy SYMBOL 185 \f "Symbol" \s 14 ? SYMBOL 198 \f "Symbol" \s 14 AE SYMBOL 222 \f "Symbol" \s 14 TH x(ya) = (xy)a.Aiiiii?o?ciii X-iiaeoey A a X-iiaeoeue B caaoueny aiiiii?o?ci aaaeaaeo a?oi f : A SYMBOL 174 \f "Symbol" \s 14 ® B oaeee, uiSYMBOL 34 \f "Symbol" \s 14 " o SYMBOL 206 \f "Symbol" \s 14 I X SYMBOL 34 \f "Symbol" \s 14 " a SYMBOL 206 \f "Symbol" \s 14 I A f(oa) = of(a).Eaoaai??y X-iiaeoe?a iicia/a?oueny /a?ac Mod X.Aeey aeaiiai /anoeiaiai a?oii?aea X( SYMBOL 215 \f "Symbol" \s 14 * ) ?icaeyiaii iai?aa?oio SYMBOL 83 \f "Symbol" \s 14 S X( SYMBOL 42 \f "Symbol" \s 14 * ), ii?iaeaeaio iiiaeeiith X c aecia/ath/eie ni?aa?aeiioaiiyie aeaeyaeoo SYMBOL 42 \f "Symbol" \s 14 * y = oy,aea o,o SYMBOL 206 \f "Symbol" \s 14 I X ? oy SYMBOL 185 \f "Symbol" \s 14 ? SYMBOL 198 \f "Symbol" \s 14 AE . C a?aeiieo aeanoeainoae iai?aa?oie, ui caaeaia aecia/ath/eie ni?aa?aeiioaiiyie, aeo?ea?Eaia 2.1.1. Eaoaai??y iai?aa?oi Sem yaey?oueny ?aoeaeoeaiith i?aeeaoaai???th a eaoaai??? /anoeiaeo a?oii?ae?a PG; oi/i?oa, SYMBOL 83 \f "Symbol" \s 14 S X yaey?oueny iai?aa?oiiaei ?aoeaeoi?ii /anoeiaiai a?oii?aea X, a i?e?iaeia a?aeia?aaeaiiySYMBOL 101 \f "Symbol" \s 14 e : X SYMBOL 174 \f "Symbol" \s 14 ® SYMBOL 83 \f "Symbol" \s 14 S X– ?aoeaeoi?iei ii?o?ciii.E??i oiai:Eaia 2.1.2. Eaoaai??? Mod X ? Mod SYMBOL 83 \f "Symbol" \s 14 S X yaeythoueny ?ciii?oieie.Iane?aeie 2.1.3. Mod X yaey?oueny aaaeaaith eaoaai???th, ui i?noeoue aeineoue aaaaoi ?i'?eoeaieo ? i?iaeoeaieo ia'?eo?a.Iaaeae? ie oe?eaaeoeiinue o?euee? oeie /anoeiaeie a?oii?aeaie, ye? yaeythoueny i?aeiiiaeeiaie iai?aa?oi.Iaoae S – aoaeue-yea iai?aa?oia. Iacaaii i?aeiiiaeeio X SYMBOL 205 \f "Symbol" \s 14 I S ei?iai iai?aa?oie S, yeui S = SYMBOL 225 \f "Symbol" \s 14 a X SYMBOL 241 \f "Symbol" \s 14 n ? aeeaaeaiiy X aei S ?iaeoeo? ?ciii?o?ci S SYMBOL 64 \f "Symbol" \s 14 @ SYMBOL 83 \f "Symbol" \s 14 S X. Eaaei aeiaanoe, ui X yaey?oueny ei?iai a S oiae? ? o?eueee oiae?, eieeS= SYMBOL 225 \f "Symbol" \s 14 a X | xy = z (x, y, z SYMBOL 206 \f "Symbol" \s 14 I X) SYMBOL 241 \f "Symbol" \s 14 n .Iai?eeeaae, iai?aa?oia S yaey?oueny nai?i ei?iai, ine?eueee S = SYMBOL 225 \f "Symbol" \s 14 a S SYMBOL 241 \f "Symbol" \s 14 n . sseui caaeaia aeia?eueia ciaaaeaiiy iai?aa?oieS = SYMBOL 225 \f "Symbol" \s 14 a a1, SYMBOL 188 \f "Symbol" \s 14 1/4 , am | P1 = Q1, SYMBOL 188 \f "Symbol" \s 14 1/4 , Pn = Qn SYMBOL 241 \f "Symbol" \s 14 n ,oi i?aeiiiaeeia, ui neeaaea?oueny c on?o ii?iaeaeoth/eo aeaiaio?a a1, SYMBOL 188 \f "Symbol" \s 14 1/4 , am ? on?o i?aene?a ne?a Pi ? Qi (1 SYMBOL 163 \f "Symbol" \s 14 F i SYMBOL 163 \f "Symbol" \s 14 F n) a aaaooe? a1, SYMBOL 188 \f "Symbol" \s 14 1/4 , am, yaey?oueny ei?iai (i?e/iio eaaei aa/eoe, ui eiaeiee ei??iue iiaeia iaea?aeaoe aiaeia?/iei niiniaii).Ia?oei e?ieii o oeueiio iai?yieo ? aecia/aiiy iaeiiaei??iiai /anoeiaiai eieaioethaa (aai X-eieaioethaa) ye ooieoe?? ia o?eniaai?e i?aeiiiaeei? X SYMBOL 204 \f "Symbol" \s 14 I S, ui ii?iaeaeo? iai?aa?oio S. I?e oeueiio cia/aiiy /anoeiaiai eieaioethaa aa?ooueny c aeayeiai X-iiaeoey A. Aeae?, iicia/eii /a?ac Xn iiiaeeio on?o iaai??a(n ?ac?a)o yeeo xi xi+1…xj SYMBOL 206 \f "Symbol" \s 14 I X aeey aoaeue-yeeo i, j oaeeo, ui 1 SYMBOL 163 \f "Symbol" \s 14 F i SYMBOL 163 \f "Symbol" \s 14 F j SYMBOL 163 \f "Symbol" \s 14 F n. Oiae? n-aei??iee /anoeiaee eieaioetha aecia/a?oueny ye a?aeia?aaeaiiy Xn o A. Aecia/ath/e cae/aeiei caniaii eia?aie/i? aiiiii?o?cie, ie iaea?aeo?ii a?oie /anoeiaeo eiaiiieia?e Hn(S, X, A). *anoeiieie aeiaaeeaie oe??? eiino?oeoe?? yaeythoueny AI-eiaiiieia?? (i?e X = S) ? 0-eiaiiieia?? (yeui S i?noeoue 0 ? X = S \ 0).Aeey i?aeiiiaeeie X iai?aa?oie S, ui ?icaeyaea?oueny ye /anoeiaee a?oii?ae, ?aoeaeoi?iee ii?o?ci(: X ( (X,i/aaeaeii, yaey?oueny aeeaaeaiiyi. Oiio X iiaeia oaeiae ?icaeyaeaoe ye i?aeiiiaeeio a (X, ? i?e oeueiio iiiaeeie Xn ia ci?iyoueny. Ioaea, ia? i?noea ?ciii?o?ciHn (S, X, A) ( Hn ((X, X, A),?, oaeei /eiii, i?e aea/aii? /anoeiaeo eiaiiieia?e iiaeia iaiaaeeoeny aeiaaeeii, eiee X – ei??iue iai?aa?oie S.Aeeaaeaiiy X SYMBOL 204 \f "Symbol" \s 14 I S ?iaeoeo? aiiiii?o?cie?ciii?o?ciaie i?e n > 0?

– ?ciii?o?ci.

– iiiiii?o?ci.

iiaea ia aooe ?ciii?o?ciii (a?aeiia?aeiee i?eeeaae iaaaaeaii a e?ioe?
oeueiai ?icae?eo).

Ia aea/aiiy /anoeiaeo eiaiiieia?e iai?aa?oie aieeaa? ?nioaaiiy a i?e
iaeeie/iiai aeaiaioo. Iai?eeeaae, i?e aeeth/aii? iaeeieoe? aei ei?aiy
oneeaaeith?oueny, acaaae? eaaeo/e, i?ioean ia/eneaiiy /anoeiaeo
eiaiiieia?e. Oiio i?aaenoaaey?oueny aeioe?eueiei ?icaeyiooe ie?aii
niaoeeo?/i? aeanoeaino? eiaiiieia?e iiii?ae?a. Oaea aeine?aeaeaiiy
i?iaaaeaii a ?icae?e? 2.2.

Iaoae S – aeayeee iiii?ae c iaeeieoeath 1, X – eiai i?aeiiiaeeia, ui
eiai ii?iaeaeo? (yea ia iaia’yceiai ? ei?aiai) ? i?noeoue 1, A –
aeia?eueiee oi?oa?iee X-iiaeoeue. Aaaaeaii iicia/aiiy T = (X \ 1(.

Oai?aia 2.2.1. Iaoae aeeiio?oueny ianooiia oiiaa: yeui x, y SYMBOL 206
\f “Symbol” \s 14 I X ? xy = 1, oi x = y = 1. Oiae? a?aeia?aaeaiiy

,

, yaey?oueny ?ciii?o?ciii aeey on?o n SYMBOL 179 \f “Symbol” \s 14 ?
0.

Ca?aene, cie?aia, aeieeaa?, ui ciai?oi? i?e?aeiaiiy iaeeieoe? aei
iai?aa?oie ia aieeaa? ia ?? /anoeia? eiaiiieia??:

Iane?aeie 2.2.2. Iaoae U = (Y( – aoaeue-yea iai?aa?oia, U1 (a?aeiia?aeii
Y1) – ?acoeueoao ciai?oiueiai i?e?aeiaiiy aei U iaeeieoe? (a?aeiia?aeii
Y1 = Y ( {1}). Oiae?

Hn (U, Y, A) ( Hn (U1, Y1, A).

A?aecia/eii, ui iaiaaeaiiy ia X a oai?ai? 2.2.1 ? ?noioiei. sse i?eeeaae
iaaaaeaii oaeee oe?eaaee oaeo:

I?iiiceoe?y 2.2.4. Iaoae G – ne?i/aiia a?oia. Oiae?

Hn (G,G \{1}, A) = 0

aeey aoaeue-yeiai G-iiaeoey A i?e n ( |G|.

Aeey ii??aiyiiy iaaaaea?ii, ui AI-eiaiiieia?? a?oie ne?i/aiiiai ii?yaeeo
caeeoathoueny iao?ea?aeueieie i?e aeia?eueiiio, ye caaaiaeii aaeeeiio,
n.

O oeueiio ae ?icae?e? aaiaeeoueny iiiyooy ii?iae?ciaaieo /anoeiaeo
eiaiiieia?e. A naia, /anoeiaee eieaioetha f SYMBOL 206 \f “Symbol” \s
14 I Cn( S, X, A) iaceaa?oueny ii?iae?ciaaiei, yeui f(x1,…, xn) = 0 ye
o?eueee xi = 1 aeey aeayeiai i SYMBOL 163 \f “Symbol” \s 14 F n.
?noioiei niiniaii aecia/athoueny a?oie ii?iae?ciaaieo X-eiaiiieia?e, ye?
aoaeaii iicia/aoe /a?ac NHn (S, X, A). Ianooiia noaa?aeaeaiiy ?
ocaaaeueiaiiyi aeia?a a?aeiiiai ?acoeueoaoo aeey eiaiiieia?e a?oi [5]:

Oai?aia 2.2.6. sseui i?aeiiiaeeia X SYMBOL 204 \f “Symbol” \s 14 I S
caaeiaieueiy? oiia? oai?aie 2.2.1, oi

aeey on?o n SYMBOL 179 \f “Symbol” \s 14 ? 0.

A?eueo iiaio ?ioi?iaoe?th i?i /anoeia? eiaiiieia?? iiaeia iaea?aeaoe ca
aeiiiiiaith eiino?oeoe?? eio?i?/ieo eiaiiieia?e, cai?iiiiiaaii? I.
Aa??ii ? Aeae. Aaeii [8, 9]. Iaiao?aei?noue o ?? aeei?enoaii?
iiynith?oueny oei, ui /anoeia? eiaiiieia?? iai?aa?oi, acaaae? aiai?y/e,
ia ? iio?aeiei ooieoi?ii, ? aei ieo ia iiaeia oaeeoe oaoi?eo Ea?oaia –
Aeeaiaa?aa. I?eoyaiaiiy ae oai??? Aa??a – Aaea aeicaiey? aecia/eoe
caaaeueiee i?aeo?ae aei aea/aiiy /anoeiaeo eiaiiieia?e.

Aeey oeueiai a ?icae?e? 2.3 aecia/a?oueny eaoaai??y PSem, ia’?eoaie
yei? ? ia?e (T, Y), aea Y – i?aeiiiaeeia a iai?aa?oi? T, a ii?o?ci

, aeey yeiai SYMBOL 97 \f “Symbol” \s 14 a (Y) i?noeoueny a Z.

), aea

= { SYMBOL 255 \f “Symbol” \s 14 y y1… SYMBOL 255 \f “Symbol” \s 14 y
yn | ( y1, …, yn ) SYMBOL 206 \f “Symbol” \s 14 I Yn }

Oey a?aeiia?aei?noue i?iaeiaaeo?oueny aei aiaeiooieoi?a G eaoaai???
PSem, ? i?ney aecia/aiiy i?aeoiaeei niiniaii i?e?iaeieo ia?aoai?aiue

SYMBOL 100 \f “Symbol” \s 14 d : G SYMBOL 174 \f “Symbol” \s 14 ® G 2
? SYMBOL 101 \f “Symbol” \s 14 e : G SYMBOL 174 \f “Symbol” \s 14
® IPSem

ie iaea?aeo?ii eio??eeo (G, SYMBOL 101 \f “Symbol” \s 14 e , SYMBOL
100 \f “Symbol” \s 14 d ).

) o eaoaai??? PSem SYMBOL 175 \f “Symbol” \s 14 ? S, caaaeyee /iio a
eaoaai??? PSem SYMBOL 175 \f “Symbol” \s 14 ? S aecia/a?oueny ooieoi?
eiaiiieia?e Hn(T, Y, A)G a?ae a?aoiaioa (T, Y). Oey eiino?oeoe?y ? aea?
ooeaia iienaiiy /anoeiaeo eiaiiieia?e o oa?i?iao oai??? Aa??a – Aaea:

Oai?aia 2.3.4. Hn(T, Y, A)G SYMBOL 64 \f “Symbol” \s 14 @ Hn+1(T, Y,
A) aeey aoaeue-yeeo n>0.

Io?eiai? ?acoeueoaoe aeicaieythoue iai aeei?enoiaoaaoe /anoeia?
eiaiiieia?? aeey ia/eneaiiy AI-eiaiiieia?e o oeo aeiaaeeao, eiee
aaea?oueny a?aeooeaoe a aeai?e iai?aa?oi? “aeia?ee” ei??iue. Oeae
ca’ycie anoaiiaeth?oueny a ?icae?eao 2.4 ? 2.5.

A ?icae?e? 2.4 aaiaeeoueny iiiyooy eaiiie/iiai ei?aiy oa
?icaeyaeathoueny eiai aeanoeaino?, iaiao?aei? aeey iiaeaeueoiai. Naia,
iaoae X – ei??iue iai?aa?oie S. Cia?aaeaiiy s = x1… xn aeaiaioa s
SYMBOL 206 \f “Symbol” \s 14 I S o aeaeyae? aeiaooeo aeaiaio?a x?
SYMBOL 206 \f “Symbol” \s 14 I X, oaeiai, ui xi xi+1 … xj SYMBOL 206
\f “Symbol” \s 14 I X aeey aoaeue-yeeo i, j, caaeiaieueiyth/eo
ia??aiinoyi 1 SYMBOL 163 \f “Symbol” \s 14 F i < j SYMBOL 163 \f "Symbol" \s 14 F n, iacaaii ?aaeoeiaaiei ?iceeaaeaiiyi. Ei??iue X iacaaii eaiiie/iei, yeui eiaeiee aeaiaio ?c S ia? ?ae?ia ?aaeoeiaaiaia ?iceeaaeaiiy.Iai?eeeaae, iiiaeeia an?o aeaiaio?a iai?aa?oie S yaey?oueny eaiiie/iei ei?aiai. Aacen naiaiaeii? iai?aa?oie F = (a1,(, an | (( oaeiae yaey?oueny, cae/aeii, eaiiie/iei ei?aiai. Iaio o?ea?aeueiee i?eeeaae eaiiie/iiai ei?aiy aea? i?aeiiiaeeia naiaiaeii? iai?aa?oieB = {b (i, j,() = ai aj( | i ( j ( (} ( F,yea ii?iaeaeo? F c aecia/ath/eie ni?aa?aeiioaiiyieb (i, j,() b (k, l,() = b (i, j,(, k, l,()i?e i ( j ( (. ( k ( l ( (.Aeey ia?aa??ee ei?aiy ia eaiiie/i?noue iai iio??aiee iaeei ?acoeueoao c [36]. Noiniaii aei iaoi? neooaoe?? oai?aia 1 oe??? noaoo? oi?ioeth?oueny oae:Eaia 2.4.1. Iaoae X – ei??iue iai?aa?oie S = (M ( R(, ui caaeiaieueiy? oiiaai:1) M ( X;2) eiaeia aecia/ath/a neiai c R i?noeoueny a X;3) aeey aoaeue-yeeo ?eaiaio?a a, b, c ( S c oiai, ui ab, bc ( X aeieeaa? abc ( X.Oiae? X yaey?oueny eaiiie/iei.Ia?aoo?, iaeeaaeaii ua iaeio aeiaeaoeiao aeiiao ia X. Ei??iue X iacaaii J-ei?aiai, yeui aeey aoaeue-yeeo x, y, z SYMBOL 206 \f "Symbol" \s 14 I X ?c xy = x, yz = z aeieeaa? xz SYMBOL 206 \f "Symbol" \s 14 I X.Iai?eeeaae, a iai?aa?oi? ?c nei?i/aiiyi aac iaeeieoe? eiaeiee ei??iue yaey?oueny J-ei?aiai.Iane?aeie 2.4.4. Iaoae X – eaiiie/iee J-ei??iue iai?aa?oie S. sseui x1,(, xn ( X ? xixi+1 ( X aeey on?o 1 ( i ( n-1, oi (x1,(, xn) ( Xn.Ianooiia noaa?aeaeaiiy yaey?oueny iniiaiei ?acoeueoaoii ae?oai? aeaae:yaey?oueny ?ciii?o?ciii aeey on?o n SYMBOL 179 \f "Symbol" \s 14 ? 0.Iniiao aeiaaaeaiiy oe??? oai?aie neeaaea? iiaoaeiaa noyaoth/i? aiiioii??, i?ae?a?aii? iaeaaeiei /eiii.sse ?ethno?aoe?th canoinoaaiiy io?eiaieo ?acoeueoao?a i?i /anoeia? eiaiiieia?? o ?icae?e? 2.6 ia/eneaii AI-eiaiiieia?? aeayeeo oei?a iai?aa?oi.IaoaeS = (a, b1, b2 , … | aP= Q (– oaea iai?aa?oia, ui aecia/aeuei? neiaa P ? Q ia i?noyoue e?oa?e a, ? Si? iicia/a? iai?aa?oio, aioe?ciii?oio iai?aa?oi? S.Oai?aia 2.6.2. Hn(S, A) = 0 aeey aoaeue-yeiai S-iiaeoey A ? aeey aeia?eueieo n SYMBOL 179 \f "Symbol" \s 14 ? 2.Oai?aia 2.6.2 aea? na??th eiio?i?eeeaae?a aei a?iioace I?o/aeea (aeea. ieae/a).Eiaiiieia?? aioe?ciii?oii? iai?aa?oieSi? = < a, b1, b2 , … | Pa = Q >

iiaoaeiaai? neeaaei?oa. Aeey ?oiueiai iienaiiy iai aoaea c?o/ii aaanoe
aecia/aiiy aiaeiaa iio?aeii? Oiena [4] aeey iai?aa?oi.

Iaoae F = (b1, b2, (( (( – aeia?eueia naiaiaeia iai?aa?oia. Iaoae
aeaiaio x ( F caienaii o aeaeyae?

x = x1 bi x2 bi ( xn-1 bi xn,

aea neiaa xk ( F ia i?noyoue aoeae bi. Iio?aeiith neiaa x ii bi iacaaii
aeaiaio iai?aa?oiiai? aeaaa?e ZF1:

oi

Oai?aia 2.6.6. Aeey aoaeue-yeiai Si?-iiaeoey A

a) H2 (Si?, A) SYMBOL 64 \f “Symbol” \s 14 @ A /B, aea

a) Hn (Si?, A) = 0 aeey on?o n SYMBOL 179 \f “Symbol” \s 14 ? 3.

?icaeyiaii oaia? ?ioee i?eeeaae.

Iaoae iai?aa?oia T ii?iaeaeo?oueny nai?th i?aeiai?aa?oiith U ? aeaiaioii
p SYMBOL 207 \f “Symbol” \s 14 I U oaeei /eiii, ui

T = (U, p | Up = p( (p
SYMBOL 207 \f “Symbol” \s 14 I U),

? Top – iai?aa?oia, aioeiciii?oia aei T.

Oai?aia 2.6.7. Aeey aoaeue-yeiai T-iiaeoey A

a) H1 (T, A) SYMBOL 64 \f “Symbol” \s 14 @ A /( p – 1)A,

a) Hn (T, A) = 0 aeey on?o n SYMBOL 179 \f “Symbol” \s 14 ? 2.

Oai?aia 2.6.8. Iaoae A – aeia?eueiee Top-iiaeoeue, A1 – aaeeoeaia a?oia
iiaeoey A, ui ?icaeyaea?oueny ye Top-iiaeoeue ?c o?ea?aeueiei
iiiaeaiiyi. Aiiiii?o?cie

SYMBOL 121 \f “Symbol” \s 14 y n: Hn (Top, A) SYMBOL 174 \f “Symbol”
\s 14 ® Hn (U, A),

ui ?iaeoeiaai? aeeaaeaiiyi U SYMBOL 174 \f “Symbol” \s 14 ® Top,
aeeth/athoueny aei aeiaai? oi/ii? iine?aeiaiino?

Oai?aie 2.6.7 ? 2.6.8 aeathoue iiaeeea?noue iiaoaeoaaoe i?eeeaae
iai?aa?oie, ui ia? a eaoaai??? e?aeo iiaeoe?a eiaiiieia?/io aei??i?noue,
aei??aithth/o 1, a a eaoaai??? i?aaeo iiaeoe?a – eiaiiieia?/io
aei??i?noue, aei??aithth/o iane?i/aiiino?. A naia, a iiia?aaei?o
oai?aiao a?cueiaii aaeeoeaio a?oio e?eueoey Z9 ye A, a ioeueoeie?eaoeaio
a?oio eiai ia?aoeieo aeaiaio?a – ye U. Ae?y U ia A ni?aiaaea? ?c
iiiaeaiiyi a e?eueoe? Z9. Oiae? H n (T, A) = 0 ? Hn (Top, A) ( Z3 i?e n
SYMBOL 179 \f “Symbol” \s 14 ? 2.

Aeaao 3 i?enay/aii aeine?aeaeaiith eiaiiieia?/ii? aei??iinoe iai?aa?oi
(ia?aaaaeii ?c nei?i/aiiyi). Eiaiiieia?/ia aei??i?noue iai?aa?oie S
iicia/a?oueny /a?ac cd S ? ?icoi??oueny a iaoiio eiioaeno? ye
i?i?iaeueia oe?ea iaa?ae’?iia /enei n, oaea ui Hn+1 (S, A) = 0 aeey
aoaeue-yeiai S-iiaeoey A.

O ?icae?e? 3.1 aea/athoueny aiiieia?/i? aeanoeaino? i?aeiai?aa?oi
aaeeoeaii? iai?aa?oie Nr iaa?ae’?iieo oe?ei/enaeueieo aaeoi??a..
I?aeiai?aa?oia S SYMBOL 204 \f “Symbol” \s 14 I Nr iaceaa?oueny
ia’?iiith, yeui aiia ia i?noeoueny o aeaniiio i?aei?inoi?? i?inoi?o Rr,
? ?yniith, yeui ciaeaeaoueny oaeee aaeoi? f , ui f + e(?) SYMBOL
206 \f “Symbol” \s 14 I S aeey on?o i?o?a e(?).

I?iiiceoe?y 3.1.4. Eiaeia ia’?iia iai?aa?oia S SYMBOL 204 \f “Symbol”
\s 14 I Nr ?ciii?oia ?yni?e.

Iicia/eii /a?ac [Con S] noeoii?noue oe?ei/enaeueieo oi/ie, ui i?noyoueny
a iioeeiio caieiaiiio eiion?, iaoyaiooiio ia S (o ae?eniiio i?inoi??
Rr).

Oai?aia 3.1.6. Eiaeia ne?i/aiii ii?iaeaeaia ?ynia i?aeiai?aa?oia S
SYMBOL 204 \f “Symbol” \s 14 I Nr i?noeoue ?aeaae aeaeo I = v + [Con S]
aeey aeayeiai aeaiaioa v SYMBOL 206 \f “Symbol” \s 14 I S.

Oea noaa?aeaeaiiy ocaaaeueith? a?aeiio aeanoea?noue i?aeiai?aa?oi ?c N,
a?aeiia?aeii aei yeiai eiaeia oaea i?aeiai?aa?oia ?ciii?oia
i?aeiai?aa?oi?, yea i?noeoue i?ii?iue [n, SYMBOL 165 \f “Symbol” \s 14
Y ) aeey aeayeiai iaoo?aeueiiai n.

, aea (p1,(, pr) ( S. Aeey nei?i/aiiy aaaaeaii iicia/aiiy

,

aea p = (p1,(, pr).

Ca?aeii c i?iiiceoe??th 3.1.4 ie iiaeaii iaiaaeeoeny aeiaaeeii, eiee S –
?ynia iai?aa?oia. Cao?ene?o?ii aeaiaio f ( S, aeey yeiai f + e(i) ( S
i?e on?o i ( r.

Iaaaaea?ii, ui ooiaeaiaioaeueiei ?aeaaeii IP iai?aa?oiiaiai e?eueoey ZS
caaoueny yae?i aiiiii?o?cio

Oaeei /eiii, ?aeaae IP ye iiaeoeue iaae ZS ii?iaeaeoaoueny on?ia

eeaiaioaie aeaeyaeo s – 1 (s ( P).

Oai?aia 3.1.7. Ooiaeaiaioaeueiee ?aeaae ISM iai?aa?oiiaiai e?eueoey ZSM
ii?iaeaeo?oueny ye ZSM-iiaeoeue iiiai/eaiaie

Iane?aeie 3.1.8. Ooiaeaiaioaeueiee ?aeaae aeia?eueii? iai?aa?oie S ( Nr
yaey?oueny ne?i/aiii ii?iaeaeaiei.

I?aee?aneeii, ui iane?aeie 3.1.8 caeeoa?oueny ni?aaaaeeeaei ? aeey
iane?i/aiii ii?iaeaeaieo i?aeiai?aa?oi.

A?eueo aeaoaeueiee ?icaeyae iaeiiaei??iiai aeiaaeeo aeicaiey? aeaoe
iiaia iienaiiy eiiooaoeaieo iai?aa?oi eiaiiieia?/iie aei??iino? 1 ?c
nei?i/aiiyi:

Oai?aia 3.1.9. Aeey eiiooaoeaiie iai?aa?oie S ?c nei?i/aiiyi

cd S = 1 oiae? ? o?eueee oiae?, eiee S ? ?ciii?oiith aai aei a?oie Z,
aai aei i?aeiai?aa?oie iai?aa?oie N.

?icae?e 3.2 ? aeiiii?aeiei (aeey ?icae?eo 3.3), oi/a ? i?aaenoaaey?
naiino?eiee ?ioa?an.

Ii-ia?oa, ooo aeaii iaeei e?eoa??e aeey eiaiiieia?/ii? aei??iino?
iiaeoey:

Eaia 3.2.1. Iaoae R – aoaeue-yea e?eueoea, A – e?aee iiaeoeue iaae R, (n
– eia?aie/iee iia?aoi? i?i?eoeaii? ?acieueaaioe iiaeoey A. Oiae? (n
iiaeia ?icaeyaeaoe ye eioeeee, ui iaeaaeeoue aei Zn+1(A, Im(n). Eioeeee
(n yaey?oueny eiaiiieia?/iei ioeth oiae? ? o?eueee oiae?, eiee
i?iaeoeaia aei??i?noue iiaeoey A ia ia?aaeuo? n.

Ii-ae?oaa, a oeueiio ?icae?e? aeine?aeaeaii aeanoeaino? iaeiiai oeio
nenoai ??aiyiue o iai?aa?oiao.

Iaoae S iicia/a? iai?aa?oio ic nei?i/aiiyi eiaiiieia?/ii? aei??iinoe 1.
Iacaaii nenoaio ??aiinoae o iai?aa?oi? S

oeeee?/iith (ooo n >1). Oeeee?/ia nenoaia caaoueny ?aceiaeeiith, yeui
ai SYMBOL 206 \f “Symbol” \s 14 I aj S aeey aeayeeo i SYMBOL 185 \f
“Symbol” \s 14 ? j, ? i?eaiaeeiith, yeui ai S SYMBOL 199 \f “Symbol”
\s 14 C aj S SYMBOL 185 \f “Symbol” \s 14 ? SYMBOL 198 \f “Symbol”
\s 14 AE aeey aeayeeo i, j, oaeeo, ui i SYMBOL 185 \f “Symbol” \s
14 ? j, i SYMBOL 185 \f “Symbol” \s 14 ? j SYMBOL 177 \f “Symbol”
\s 14 ± 1 (mod n). Oeeee?/io nenoaio i?e n SYMBOL 163 \f “Symbol” \s
14 F 3 ie aaaaea?ii iai?eaiaeeiith.

Oai?aia 3.2.4. Oeeee?/ia nenoaia (1) i?eaiaeeia i?e n > 3.

Oai?aia 3.2.5. sseui n = 3, oi aeey nenoaie (1) ciaeaeooueny oae?
aeaiaioe zi SYMBOL 206 \f “Symbol” \s 14 I S (1 SYMBOL 163 \f
“Symbol” \s 14 F i SYMBOL 163 \f “Symbol” \s 14 F 3), ui a1 z1 = a2
z2 = a3 z3.

Oe? oai?aie aeiioneathoue oiiieia?/io ?ioai?aoaoe?th. ?icaeyiaii
neiie?oe?aeueiee eiiieaen, aa?oeiaie yeiai yaeythoueny aeaiaioe
iai?aa?oie S, a n-i??ieie a?aiyie – iaai?e (a1 , …, an+1 ), ai
SYMBOL 206 \f “Symbol” \s 14 I S, aeey yeeo

Oiae? eiaeiee caieiooee oeyo o oeueiio eiiieaen? noyao?oueny. Cie?aia

yeui S ? iiii?aeii, oi oaeee eiiieaen aoaea e?i?eii ca’yciei ? eiai
ooiaeaiaioaeueia a?oia o?ea?aeueia.

Ca aiaeia??th c a?iioacith Aai? – Aeeaiaa?aa aeey a?oi (iiceoeaia
ae??oaiiy yei? i?ci?oa iaea?aeaei iacao oai?aie Noiee?iana – Noiia [1])
A. I?o/aee [18] i?eionoea, ui iai?aa?oia c? nei?i/aiiyi eiaiiieia?/ii?
aei??iino? 1 iiaeiia aooe oae caaiith /anoeiai naiaiaeiith (oiaoi
naiaiaeiei aeiaooeii naiaiaeii? a?oie ? naiaiaeii? iai?aa?oie).

O noaooyo [24] ? [26] aeena?oaioii iiaoaeiaaii eiio?i?eeeaaee aei
a?iioace I?o/aeea. E??i oiai, o [26] noi?ioeueiaaii iiaa i?eiouaiiy
(iineaaeaia a?iioaca I?o/aeea): yeui iai?aa?oia c? nei?i/aiiyi ia?
eiaiiieia?/io aei??i?noue, aei??aithth/o 1, oi aiia aeeaaea?oueny a
a?oio (i?e/iio inoaiiy aaoiiaoe/ii yaey?oueny naiaiaeiith ca?aeii c
oai?aiith Noiee?iana – Noiia).

O ?icae?e? 3.3 aeaii iiceoeaia ae??oaiiy ineaaeaii? a?iioace I?o/aeea:

Oai?aia 3.3.3. Iai?aa?oia c? nei?i/aiiyi eiaiiieia?/iie aei??iino? 1
aeeaaea?oueny aei naiaiaeii? a?oie.

Aeiaaaeaiiy oai?aie 3.3.3 caniiao?oueny ia ?acoeueoaoao iiia?aaeiueiai
?icae?eo, a oaeiae ia iaei?e aeinoaoi?e oiia? aeeaaeaiiy iai?aa?oie aei
a?oie,

yeo iaea?aeaa I. Aoei.

A?aecia/eii, ui c ?acoeueoao?a ?icae?eo 2.6 aeieeaa?, ui cai?ioia
noaa?aeaeaiiy iaa??ia.

Iniiai? ?acoeueoaoe oe??? aeaae iioae?eiaaii a [28, 29, 34, 35, 37].

?ioee i?aeo?ae aei aeine?aeaeaiiy iai?aa?oi eiaiiieia?/ii? aei??iinoe 1
(ia iaia’yceiai ?c nei?i/aiiyi) cae?enith?oueny a aeaa? 4. A?i
caniiaaiee ia aeei?enoaii? iiiyooy ?aoeaeoeaii? i?aeeaoaai??? ?
?icaeyaea?oueny a ?icae?e? 4.1. sseui D – ?aoeaeoeaia i?aeeaoaai?ey
eaoaai??? iai?aa?oi Sem (iai?eeeaae, i?aeeaoaai?ey a?oi, iai?ano?oeoo?
a?oi, oe?eeii i?inoeo, ?iaa?nieo aai ee?ooi?aeiaeo iai?aa?oi), oi
?aoeaeoi?iee ii?o?ci ?iaeoeo? aiiiii?o?ci a?oi eiaiiieia?e

SYMBOL 101 \f “Symbol” \s 14 e n : Hn (R (S) , A) SYMBOL 174 \f
“Symbol” \s 14 ® Hn (S, A),

aea R(S) – ?aoeaeoi? iai?aa?oie S a eaoaai??? D.

C aeei?enoaiiyi aeia?a a?aeiieo ca’yce?a i?ae iaeiiaei??ieie
eiaiiieia?yie ? iai?ai?yieie aeiaooeaie iaea?aeaii oae? ?acoeueoaoe
(ieae/a /a?ac A SYMBOL 208 \f “Symbol” \s 14 ? R (S) iicia/aii
iai?ai?yiee aeiaooie):

Oai?aia 4.1.1. Iaoae S – aeia?eueia iai?aa?oia, A – iiaeoeue iaae R (S).
sseui A SYMBOL 208 \f “Symbol” \s 14 ? R (S) SYMBOL 206 \f “Symbol”
\s 14 I D, oi SYMBOL 101 \f “Symbol” \s 14 e 1 yaey?oueny
?ciii?o?ciii.

Iane?aeie 4.1.2 Iaoae D – ?aoeaeoeaia i?aeeaoaai??y eaoaai??? Sem, S
SYMBOL 206 \f “Symbol” \s 14 I Sem, R(S) – D-?aoeaeoi? iai?aa?oie S.

1) sseui A SYMBOL 208 \f “Symbol” \s 14 ? R(S) SYMBOL 206 \f “Symbol”
\s 14 I D aeey aoaeue-yeiai R(S)-iiaeoey A, oi SYMBOL 101 \f “Symbol”
\s 14 e 2 yaey?oueny iiiiii?o?ciii.

2) sseui R(S) ? iiii?aeii ? A SYMBOL 208 \f “Symbol” \s 14 ? R(S)
SYMBOL 206 \f “Symbol” \s 14 I D aeey aoaeue-yeiai oi?oa?iiai
R(S)-iiaeoey A, oi SYMBOL 101 \f “Symbol” \s 14 e 2 yaey?oueny
iiiiii?o?ciii.

Cie?aia , oea aoaea oae, yeui D yaey?oueny eaoaai???th a?oi, oe?eeii
i?inoeo iai?aa?oi aai ee?ooi?aeiaeo iai?aa?oi (i?iiiceoe?y 4.1.3).
Ca?aene aeieeaa?, ui aeanoea?noue “iaoe eiaiiieia?/io aei??i?noue 1”
niaaeeo?oueny ?aoeaeoi?aie oeacaieo oei?a.

Aeei?enoaiiy oaeiai i?aeoiaeo iieacaia ia i?eeeaae? iienaiiy oe?eeii
i?inoeo iai?aa?oi eiaiiieia?/ii? aei??iinoe 1.

Iaoae T = M(G; I, (; P) – oe?eeii i?inoa iai?aa?oia c
naiaea?/-iao?eoeath P = (p(i), N – ii?iaeueiee ae?eueiee a G,
ii?iaeaeaiee aeaiaioaie p(i (( ( (, i ( I), i?e/iio c oi/i?noth aei
?ciii?o?cio ie iiaeaii aaaaeaoe, ui p1i = p(1 = e.

Eaia 4.14. G/N yaey?oueny a?oiiaei ?aoeaeoi?ii iai?aa?oie T.

Oai?aia 4.1.5. sseui oe?eeii i?inoa iai?aa?oia T = M(G; I, (; P)

ia? eiaiiieia?/io aei??i?noue 1, oi:

1) oaeoi?a?oia G/N naiaiaeia;

2) a?oia G naiaiaeia;

3) iiiaeeia {p(i | ( ( 1, i ( 1}, yeui aiia ia ? ionoith, yaey?oueny
aacenii a ii?iaeaeai?e ?th (naiaiaei?e) i?aea?oi? a?oie G.

Iane?aeie 4.1.6. sseui iai?aa?oia ia? eiaiiieia?/io aei??i?noue 1, oi ??
oe?eeii i?inoee ?aoeaeoi? caaeiaieueiy? oiiaai 1)-3) oai?aie 4.1.5.

O ca’yceo c iiaeeeaeie canoinoaaiiyie aei oai??? eiaiiieia?e c’yaeeanue
iaiao?aei?noue a?eueo aeaoaeueii aea/eoe aeanoeaino? a?oiiaeo
?aoeaeoi??a iai?aa?oi. I?e oeueiio aeieea? aeayeee eean /anoeiaeo
a?oii?aeia (iacaaieo o aeena?oaoe?ei?e ?iaio? Z-ia?oi?aeaie), ui o?nii
iia’ycai? c a?aoii ae?eeiino? iai?aa?oie. Aeanoeaino? Z-ia?oi?ae?a
aeine?aeaeothoueny a ?icae?e? 4.2. Ca ?oiueith aeiiiiiaith o ?icae?e?
4.3 (oai?aia 4.3.8) ocaaaeueith?oueny iaoiae iiaoaeiae a?oiiaiai
?aoeaeoi?a aeey iai?aa?oie ?c nei?i/aiiyi, yeee cai?iiiiiaaii
Ke?ooi?aeii ? I?anoiiii [3].

*anoeiaee a?oii?ae, ui c’yaey?oueny i?e oeueiio, ia? oaeee aeae.
I?eionoeii aac oo?aoe caaaeueiino?, ui S i?noeoue iaeeieoeth. ?icaeyiaii
i???ioiaaiee a?ao c aeaiaioaie ?c S ye aa?oeiai?; a ? b niieo/ai?
?aa?ii (?c ii/aoeiaith aa?oeiith a), yeui b = ax aeey aeayeiai x
SYMBOL 206 \f “Symbol” \s 14 I S (a?ao ae?eeiino? iai?aa?oie). Ie
aoaeaii iicia/aoe oaea ?aa?i /a?ac [a, x]. Aecia/ath/e ia iiiaeei?
?aaa? P(S) /anoeiao iia?aoe?th

[a, x] [ax, y] = [a, xy],

ie ia?aoai?th?ii P(S) o /anoeiaee a?oii?ae.

E??i oiai, aeyaey?oueny c?o/iei aaanoe aeiaeaoeiaee ia’?eo K, iacaaiee
eiiieaenii Eaee iiii?aea S, – oea neiie?oe?aeueiee eiiieaen, caaeaiee ia
iiiaeei? S, aeey yeiai neiieaenaie ? an?eye? iaai?e (a0, …, an) iiia?ii
??cieo aeaiaio?a ?c S, oaeeo, ui ai+1 SYMBOL 206 \f “Symbol” \s 14 I
ai S aeey on?o i < n. Eiiieaen Eaee aecia/a?oueny a?aoii ae?eeiino? (aai, ui oa ae naia, a?oii?aeii) P(S), ?icaeyiooei o iiia?aaeiueiio ?icae?e?; a naia, n-neiieaene aca?iii iaeiicia/ii a?aeiia?aeathoue i???ioiaaiei iooyi aeiaaeeie n o a?ao? P(S).O ?icae?e? 4.4 aea/athoueny ca'ycee i?ae eiaiiieia?yie iai?aa?oie S oa ?? eiiieaeno Eaee K. O i?eiouaii?, ui S ? iiii?aeii ?c nei?i/aiiyi, yeee ia ia? ia?aoeieo iaiaeeie/ieo aeaiaio?a, io?eiaii oae? ?acoeueoaoe:Oai?aia 4.4.3. sseui A – S-iiaeoeue ?c ioeueiaei iiiaeaiiyi, oiHn (S, A) SYMBOL 64 \f "Symbol" \s 14 @ Hn-1 (K, A)aeey on?o n SYMBOL 179 \f "Symbol" \s 14 ? 2.Iane?aeie 4.4.4. sseui cd S ( n, oi Hm(K, A) = 0 aeey on?o m ( n ? aoaeue-yei? aaaeaai? a?oie A.Iiaeia io?eiaoe oaeiae aeayeo ?ioi?iaoe?th i?i aiiieia?? eiiieaeno Eaee, yea aea? a?eueo i?ici?ee ca'ycie i?ae eiai oiiieia?/iith no?oeoo?ith ? eiaiiieia?yie iiii?aea S:Iane?aeie 4.4.5. sseui cd S SYMBOL 163 \f "Symbol" \s 14 F n, oi Hm(K) = 0 aeey aoaeue-yeiai m SYMBOL 179 \f "Symbol" \s 14 ? n.Iniiai? ?acoeueoaoe oe??? aeaae iioae?eiaaii a [30, 38].Aeaao 5 i?enay/aii aeeeaaeaiith caaaeueii? oai??? eiaiiieia?e iai?aa?oi. O i?e i?iaiaeeoueny aiae?c ??ciiiai?oieo oai??e iai?aa?oiiaeo eiaiiieia?e ? aeacothoueny ca'ycee i?ae ieie. Ii?yae c ?nioth/eie canoinoaaaiiyie eiaiiieia?e iniaeeao oaaao a oe?? aeaa? i?eae?eaii eeaneo?eaoe?? oei?a eiaiiieia?e iai?aa?oi.O oe?? aeaa? ?icaeyaeathoueny o?e iniiaieo (c oi/ee ci?o aeena?oaioa) iai?yiee:– AI-eiaiiieia?? (o oiio aeaeyae?, a yeiio ?o aecia/aii a "Aiiieia?/i?e aeaaa??" A. Ea?oaiii ? N. Aeeaiaa?aii);– ??ciiiai?oi? oeie eiaiiieia?e, ui aeieeathoue i?e iienaii? iioe?aiue iai?aa?oi;– ie?ai? aeiaaeee /anoeiaeo eiaiiieia?e, ui c’yaeeeny i?e ae??oaii? aeayeeo aeaaa?a?/ieo caaea/.AENIIAEEA aeena?oaoe?ei?e ?iaio? aeine?aeaeoaaeeny aeanoeaino? eiaiiieia?e iai?aa?oi. An? oe? aeine?aeaeaiiy i?iaaaeaii aia?oa.Cai?iiiiiaaii i?eeeaaeaiiy aaaaeaieo ?ai?oa aeena?oaioii eiino?oeoe?? 0-eiaiiieia?e aei aea/aiiy aeanoeainoae iiii?aeo A?aoa?a oa neeueii i?eia?ieo ne?i/aiii aei??ieo aeaaa?.?ic?iaeaii oai??th /anoeiaeo eiaiiieia?e ? aeaii canoinoaaiiy ?o aei ia/eneaiiy iai?aa?oiiaeo eiaiiieia?e Aeeaiaa?aa – Iaeeaeia.Iaea?aeaii ??oaiiy iineaaeaii? i?iaeaie I?o/aeea i?i iai?aa?oie ?c nei?i/aiiyi eiaiiieia?/ii? aei??iino? 1.Aea/aii ca'ycee i?ae eiaiiieia?yie iai?aa?oi ? iaaieo eean?a ?oi?o ?aoeaeoi??a.Cai?iiiiiaaii iiiyooy eiiieaeno Eae? aeey iai?aa?oie oa aeine?aeaeaii eiai oiiieia?/i? oa?aeoa?enoeee.?acoeueoaoe aeena?oaoe?? iiaeooue aooe aeei?enoiaaieie aeey iiaeaeueoeo aeine?aeaeaiue eiaiiieia?e ye iai?aa?oi, oae ? ?ioeo aeaaa?a?/ieo nenoai.NIENIE E?OA?AOO?E1. A?aoi E.N. Eiaiiieiaee a?oii. – I.: Iaoea, 1987. – 384 c.2. Ea?oai A., Yeeaiaa?a N. Aiiieiae/aneay aeaaa?a. – I.: EE,1960. – 510 c.3. Keeooi?ae A., I?anoii A. Aeaaa?ae/aneay oai?ey iieoa?oii. – I.: Ie?, 1972. – 422 n.4. K?ioyee ?., Oien ?. Aaaaeaiea a oai?eth oceia. – I.: Ie?, 1967. – 348 n.5. Iaeeaei N. Aiiieiaey. – I.: Ie?, 1966. – 543 n.6. Iiaeeia A.A. I 0-eiaiiieiaeyo iieoa?oii // Na.: Oai?. e i?eee. aii?.aeeoo. o?-iee e aeaaa?a. E., Iaoeiaa aeoiea. – 1978. – N.185-188.7. Iiaeeia A.A. I i?iaeoeaiuo i?aaenoaaeaieyo iieoa?oii // Aeiee. AI ONN?, na?.A. – 1979. – N6. – N.474-478.8. Barr M., Beck J. Acyclic models and triples // In: Proc. Conf. Cat. Algebra (La Jolla, 1965), Springer. – 1966. – P.336-343.9. Barr M., Beck J. Homology and standard construction // Lect. Notes in Math. – 1969. – V. 80. – P.245-335.Cheng Charles Ching-an, Shapiro J. Cohomological dimension of an abelian monoid // Proc. Amer. Math. Soc. – 1980. – V. 80. – N4. – P.547-551.11. Clark W.E. Cohomology of semigroups via topo\-lo\-gy with an application to semigroup algebras // Commun. Algebra. – 1976. – V. 4. – P.979-997.12. Haile D.E. On crossed product algebras arising from weak cocycles // J. Algebra. – 1982. – V. 74. – P.270-279.13. Haile D.E. The Brauer monoid of a field // J.Algebra. – 1983. – V. 81. – N2. – P.521-539.14. Haile D.E., Larson R.G., Sweedler M.E. A new invariant for C over R: almost invertible cohomology theory and the classification of idempotent cohomology classes and algebras by partially ordered sets with Galois group action // Amer. J. Math. – 1983. – V. 105. – N3. – P.689-814.15. Lausch H. Cohomology of inverse semigroups // J. Algebra. – 1975. – V. -35. – N1-3. – P.273-303.16. Leech J.E. Cohomology theory for monoid congruences // HoustonJ. Math. – 1985. – V. 11. – N2. – P.207-223.17. Loganathan M. Cohomology and extensions of regular semigroups// J. Austral. Math. Soc., ser. A. – 1983. – V. 35. – N2. – P.178-193.18. Mitchell B. On the dimension of objects and categories. I. Monoids// J.Algebra. – 1968. – V. 9. – N~3. – P.314-340.19. Nico W.R. On the cohomology of finite semigroups // J. Algebra. –1969. – V. 11. – N4. – P.598-612.20. Nico W.R. Homological dimension in semigroup algebras // J.Algebra. – 1971. – V. 18. – N3. – P.404-413.21. Sweedler M.E. Weak cohomology // Contemp. Math. – 1982. – V.13. – P.109-119.?IAIOE AAOI?A CA OAIITH AeENA?OAOe??NOAOO?:22. Iiaeeia A.A. 0-eiaiiieiaee aiieia 0-i?inouo iieoa?oii //Aanoiee Oa?uee. ain. oi-oa. – aui. 46. – 1981. – N221. – N.80-85.23. Iiaeeia A.A. I au/eneaiee eiaiiieiaee iaeioi?uo iieoa?oii // Aanoiee Oa?uee. ain. oi-oa. – aui. 46. – 1981. – N221. – N.96.24.Iiaeeia A.A. Eiio?i?eia? e iaeiie aeiioaca Ieo/aeea // O?.Oaee. iao. ei-oa AI ANN?. – 1982. – O. 70. – N.52-55.25. Iiaeeia A.A. Ii?aaeaeythuea niioiioaiey e 0-iiaeoee iaae iieoa?oiiie // Na.: Oai?ey iieoa?oii e aa i?eeiae. Iieeaaee/. iieoa?oiiu. Iieoa?oiiu i?aia?aciaaiee. Ecae-ai Na?aoia. oi-oa . – 1983. – N.94-99.26. Novikov B.V. On partial cohomologies of semigroups // Semigroup Forum. – 1984. – V. 28. – N1-3. – P.355-364.27. Iiaeeia A.A. *anoe/iua eiaiiieiaee iieoa?oii e eo i?eeiaeaiey // Eca. aocia. Iaoai. – 1988. – N11. – N.25-32.28. Iiaeeia A.A. Eiiiooaoeaiua iieoa?oiiu n nie?auaieai ?acia?iinoe 1 // Iaoai. caiaoee. – 1990. – N. 48. – N1. – N.148-149.29. Iiaeeia A.A. I no?iaiee iiaeiiiaeanoa aaeoi?iie ?aoaoee, caieioouo ioiineoaeueii neiaeaiey // Oe?. aaii. na. – 1992. – N35. – N.99-103.30. Iiaeeia A.A. ?aoeaeoeaiua iiaeeaoaai?ee e eiaiiieiaee iieoa?oii // Aeiiiaiaei AI Oe?a?ie. – 1994. – N8. – N.10-12.31. Novikov B.V. On the structure of subsets of a vector lattice that are closed with respect to addition // J. Math. Sci. – 1994. – V.72. – N 4. – P.3223-3225.32. Novikov B.V. On modification of the Galois group // Filomat (Yugosl.). – 1995. – V. 9. – N3. – P.867-872.33. Iiaeeia A.A. I iiiieaea A?aoy?a // Iaoai. caiaoee. – 1995. – O. 57. – N 4. – N.633-636.34. Iiaeeoa A.A. I iieoa?oiiao eiaiiieiae/aneie ?acia?iinoe 1 // Aeiiia?ae? IAI Oe?a?ie. – 1996. – N 8. – N.6-8.35. Iiaeeoa A.A. Ia ineaaeaiiie aeiioaca Ieo/aeea // Aeiiia?ae? IAI Oe?a?ie. – 1998. – N 3. – N.26-27.36. Kashcheeva O.S., Novikov B.V. Canonic subsets in semigroups // Filomat (Yugosl.). – 1998. – V. 12. – N1. – P.21-27.37. Novikov B.V. Semigroups of cohomological dimension 1 // J. Algebra. – 1998. – V. 204. – N.2. – P.386-393.38. Novikov B.V. Quotients of cancellative semigroups // Aii?inu aeaaa?u (Aiiaeue, Aaea?onue). – 1998. – O. 13. – N.22-28.39. Novikov B.V. Partial cohomologies and canonic roots in semigroups // Iaoaiaoe/i? nooae??. – 1999. – V. 12 . – N1. – C. 7–14.40. Novikov B.V., Iordjev K. On a generalization of ideals in infinite semigroups // C.R.Acad.Bulgare Sci. – 1996. – V. 49. – N4. – P.5-8.OACE AeIIIA?AeAE:41. Iiaeeia A.A. I /anoe/iuo eiaiiieiaeyo iieoa?oii // Na.: XVI Anan. aea. eiioa?aioeey. Oacenu. – *.2, E. – 1981. – N.97-98.42. Iiaeeia A.A. I eio?ia/iie oai?ee /anoe/iuo eiaiiieiaee iieoa?oii // Na.: XVII Anan. aea. eiioa?aioeey. Oacenu niiau., Ii. – 1983. – N.175.Hiaeeia A.A. I eiaiiieiae/aneie ?acia?iinoe iaeioi?uoiieoa?oii // Na.: XVIII Anan. aea. eiioa?aioeey. Oacenu niiau. – *.2, Eeo. – 1985. – N.66.44. Iiaeeia A.A. I iiiieaea A?aoy?a // Na.: XIX Anan. aea. eiioa?aioeey. Oacenu niiau. – *.2, Eueaia. – 1987. – N.203.45. Novikov B.V. On semigroups of cohomological dimension one // In: Colloquium on Semigr. Szeged (Hung.). – 1994. – P.27.46. Novikov B.V. On modification of the Galois group // In: Algebra, Logic & Discr. Math., Nish (Yugosl.). – 1995. – P.86-87.47. Novikov B.V. The Ore complex and the semigroup dimension // Representation Theory and Computer Algebra. Kyiv, March 18 – 23. Kyiv Univ. – 1997. – P.32-33.Iia?eia A.A. Eiaiiieia?? iai?aa?oi.- ?oeiien.Aeena?oaoe?y ia caeiaoooy iaoeiaiai nooiaiy aeieoi?a o?ceei-iaoaiaoe/ieo iaoe ca niaoe?aeuei?noth 01.01.06 – aeaaa?a ? oai??y /enae.- Ee?anueeee oi?aa?neoao ?i. O. Oaa/aiea, Ee?a, 1999.Aeena?oaoe?th i?enay/aii aeine?aeaeaiith eiaiiieia?e iai?aa?oi oa ?o canoinoaaiiyi. Aea/aii aeanoeaino? iai?aa?oi eiaiiieia?/ii? aei??iino? 1, cie?aia, aeiaaaeaii iineaaeaio a?iioaco I?o/aeea. Cai?iiiiiaaii iiao eiino?oeoe?th /anoeiaeo eiaiiieia?e iai?aa?oi, iaea?aeaii ?oi? eio?i?/ia cia?aaeaiiy ? ca'ycie ?c eiaiiieia?yie Aeeaiaa?aa – Iaeeaeia. C ?oiueith aeiiiiiaith ciaeaeaii a?oie eiaiiieia?e Aeeaiaa?aa – Iaeeaeia aeayeeo eean?a iai?aa?oi ?, cie?aia, aeaii ?yae eiio?i?eeeaae?a aei a?iioace I?o/aeea. Iaaaaeaii aeei?enoaiiy /anoeiaeo eiaiiieia?e aeey eeaneo?eaoe?? neeueii i?eia?ieo anioe?aoeaieo aeaaa?, io?eiaii iia? aeanoeaino? iiii?aea A?aoa?a.Eeth/ia? neiaa: iai?aa?oie, a?oie eiaiiieia?e iai?aa?oi, /anoeia? eiaiiieia??, iiii?ae A?aoa?a, eiaiiieia?/ia aei??i?noue, ?aoeaeoeaia i?aeeaoaai??y, eaioethaiaee eiiieaen, neiie?oe?aeueiee eiiieaen.Novikov B.V. Cohomology of semigroups. Manuscript.Thesis of the dissertation for obtaining of the degree of doctor of sciences in physics and mathematics, speciality 01.01.06 – algebra and number theory. Kyiv Taras Shevchenko University, Kyiv, 1999.The thesis is devoted to investigation of semigroup cohomology and its applications. Properties of semigroups of cohomological dimension 1 are studied, in particular, the weakened Mitchell conjecture is proved. A new construction of partial cohomology is proposed, its cotriple presentation and relation to Eilenberg – MacLane cohomology is obtained. The Eilenberg – MacLane cohomology groups of some classes of semigroups are founded with the help of partial cohomology, and, in particular, the serie of counter-examples to the Mitchell conjecture is given. The using of partial cohomology for classification of the strongly primary algebras is proposed, new properties of the Brauer monoid are obtained.Key words: semigroups, cohomology groups of semigroups, partial cohomology, Brauer monoid, cohomological dimension, reflective subcategory, chain complex, simplicial complex.Iiaeeia A. A. Eiaiiieiaee iieoa?oii. – ?oeiienue.Aeenna?oaoeey ia nieneaiea o/aiie noaiaie aeieoi?a oeceei-iaoaiaoe/aneeo iaoe ii niaoeeaeueiinoe 01.01.06 – aeaaa?a e oai?ey /enae.- Eeaaneee oieaa?neoao ei. O. Oaa/aiei, Eeaa, 1999.Aeenna?oaoeey iinayuaia enneaaeiaaieth eiaiiieiaee iieoa?oii e eo i?eeiaeaieyi.Iieo/aii i?eiaiaiea 0-eiaiiieiaee e eeanneoeeaoeee neeueii i?eia?iuo aeaaa?. Aaaaeaii iiiyoea iiaeeoeeaoeee a?oiiu e i?aaeeiaeaii iino?iaiea iiiieaea A?aoy?a n iiiiuueth 0-eiaiiieiaee a?oiiu Aaeoa. I?e ii?aaeaeaiiuo oneiaeyo iaeaeaii yae?i aiiiii?oecia eiiiiiaiou iiiieaea A?aoy?a a a?oiio A?aoy?a. Iienaiu iaeioi?ua oeiu iiaeeoeeaoeee oeeeee/aneie a?oiiu i?inoiai ii?yaeea.I?aaeeiaeaia iiaay eiino?oeoeey /anoe/iuo eiaiiieiaee iieoa?oii, ii?aaeaeyaiuo n iiiiuueth /anoe/iuo ooieoeee ec iieoa?oiiu a iiaeoeue iaae iae. A nayce n oai, /oi /anoe/iua eiaiiieiaee ia yaeythony i?iecaiaeiui ooieoi?ii, aeaii eo i?aaenoaaeaiea n iiiiuueth oai?ee Aa??a – Aaea. Aaaaeaii iiiyoea eaiiie/aneiai ei?iy eae ii?iaeaeathuaai iiiaeanoaa, oaeiaeaoai?ythuaai iaeioi?ui oneiaeyi iaeiicia/iinoe ?aceiaeaiey yeaiaioia iieoa?oiiu e caaeathuaai iaeanoue ii?aaeaeaiey aeey /anoe/iuo eioeeeeia. Aeieacaii, /oi aeey eaiiie/aneeo J-ei?iae a?oiiu /anoe/iuo eciii?oiu a?oiiai eiaiiieiaee Yeeaiaa?aa – Iaeeaeia. Iieo/aiiua ?acoeueoaou eniieueciaaiu aeey au/eneaiey eiaiiieiaee Yeeaiaa?aa – Iaeeaeia iaeioi?uo eeannia iieoa?oi e, a /anoiinoe, aeai ?yae eiio?i?eia?ia e aeiioaca Ieo/aeea.Eco/aiu naienoaa iieoa?oii n nie?auaieai eiaiiieiae/aneie ?acia?iinoe 1, a /anoiinoe, aeieacaia ineaaeaiiay aeiioaca Ieo/aeea: iieoa?oiia n nie?auaieai eiaiiieiae/aneie ?acia?iinoe 1 aeeaaeuaaaony a naiaiaeioth a?oiio. A eiiiooaoeaiii neo/aa yoi oneiaea ieacuaaaony iaiaoiaeeiui e aeinoaoi/iui: eiiiooaoeaiay iieoa?oiia n nie?auaieai eiaao ?acia?iinoue 1 oiaaea e oieueei oiaaea, eiaaea iia eciii?oia iiaeiieoa?oiia a?oiiu oeaeuo /enae (a iauai neo/aa, eae iieacuaatho ii?eia?u, i?eaaaeaiiua a aeenna?oaoeee, ia?auaiea ineaaeaiiie aeiioacu Ieo/aeea iaaa?ii).?anniio?aia naycue iaaeaeo eiaiiieiaeyie iieoa?oiiu e aa ?aoeaeoi?a. Iieo/aiu oneiaey ia ?aoeaeoeaioth iiaeeaoaai?eth, i?e eioi?uo ?aoeaeoi?iue ii?oeci eiaeooee?oao eciii?oeci iaeiiia?iuo eiaiiieiaee e iiiiii?oeci aeaoia?iuo eiaiiieiaee (a /anoiinoe, oaeiauie ieacuaathony iiaeeaoaai?ee a?oii, aiieia i?inouo iieoa?oii e eeeooi?aeiauo iieoa?oii). I?aaeeiaeaia iiaay eiino?oeoeey aeey a?oiiiaiai ?aoeaeoi?a iieoa?oiiu n nie?auaieai. Ii?aaeaeaii iiiyoea eiiieaena Eyee aeey iieoa?oiiu, onoaiiaeaiu niioiioaiey iaaeaeo aai a?oiiaie neiieeoeeaeueiuo eiaiiieiaee e eiaiiieiaeyie enoiaeiie iieoa?oiiu.Eeth/aaua neiaa: iieoa?oiiu, a?oiiu eiaiiieiaee iieoa?oii, /anoe/iua eiaiiieiaee, iiiieae A?aoy?a, eiaiiieiae/aneay ?acia?iinoue, ?aoeaeoeaiay iiaeeaoaai?ey, oeaiiie eiiieaen, neiieeoeeaeueiue eiiieaen.PAGE 34PAGE 34PAGE 28

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