A J I T E E P A H J I O r H K ACeuHnap

Tou 4BunycK 4 PyKOBoaHieJii A.H.UaJimeB 1965 r.

<&AKTOPH3AUHOHHblE TEOPEMbI flJIfl HEKOTOPUX KJIACCOBKOIffiU EE3 flEMTEJffifl H7JIH. I.

JI.A.EOKyTB

§ I . B s e a e H H e

/? - HeKoiopoe accouHaiHBHoe KOJIBUO des aejiHTejien ny-JIH a c 1 . Iloa $aKiopH3aiflioHH00 Teopeiioa «nn /^ B 3108 padoieuu dyaeu noHmiaxB orwcaHHe (B HCKOTOPHX TepuHHax) unoxecTBa ^^

neHyjieBHX BJieueHioB (fl B, C, 2)) KOJiBoa R ,fljw KoiopHXcooTHomeHHe

Hanpraiep, ewiH ^ - Teno, TO HB (I) caeayei cooTHonerae:

(2)

X e /? .B nocjieHHHe row $&KTopH3amiOHHbie teopeuu (z npraeaeHHoy BH-

me ouucjie) WK aeKOTopux mapoKHX KJISCCOB KOJISK <5es zewieneft HyjmKOHOM (CM. [I] ,§ 4, CJiegciBHe I; [2], § 4 ).HiieHHO,KoH

HBHHfi BHA B06X 16TBepOK HS ^̂ flJIfl HOJIHHX $HJH>TpOBaHHEIX

c HHsepCHMi ajiropMTMOM [I] H aJifl KOJiei^ co cjiafiboi ajiropnTHOU[2]. HepBuM KB STHX KJiaccos coaepSHT, B qacTHOCTH, ajiredpH cie -

PHSOB OT HeasBeoiHux, Biopofl - CBotfoflHHe ajiredpa., ITO HS onpesejieHHH icojieii co cnadmi asropHTMoii Heno-BHieKaei, MTO B HHX BHnojraHeicH ojiezyvmn $aKTOpMsa -

reopeua.

26 JI.A.BoKyTB

TEOPEMA A, n p o H 3 B O J i B H H B s Ji e M e H T U H O -se e c T B a 'ffit , n o c T p o e H H o r o a ji H K O j i tn o n y q a e i c H u s l e i s e p K H

c n o M o m B K> c j i e f l y r a m a x o n e p a i j H f t :

2)T a e X, - H e H y j i e s H e a j i e M e H T U a s j

3) y>A (A, B,C,Z»= (#+€*,&,€,£+ XB) ,p a e Xey?^ fl+CX^O, £ + XB*O .

Ms TeopeuH A HeipyaHO BusecTH OTueqeHHyio BHme Teopeay KoHa.Teopeua A BHnojiHHeTCH He B Kaawou KOJIBUS. Hanpioiep, ona He

B KonBi^e R , KOTOpoe ecu. aJtrcOpa c 3. (eaa HCKOTO-noaeM p ) c CHCTeuofl odpasyroiUHX 1̂ ^Li^i^ij *-£•! ,n on-

JhieHHO, B 3Tou nocjieflHeii KOJIBUC R. Buno^flneTCH

TEOPEMA B . I l p o H 3 B O J i B H a f l l e T s e p i c a M H Ox e c T B a ??t n o j i y i a e i c f l M S q e i B e p K H QdH q e i s e o K

C O O T B e T C T B y I O ^ H X H C X O f l H H U C O O T H O

ra e H H H ii (3), c n o M o m B n o n e p a i ^ H t l :

I)

3 )

r a e (w^.u,^) - o f l H a H 3 q e i s e p o K (4),

X(wB-uZ)), d(^w+/J)>cL(ff) ,, ^̂ ^ ̂ 0 > ̂ O , &(/£,+ £) >

leopeuu HJIH HeKOTopax KJiaccosdes aeJiHTejieJt Hyan. I.

B $opMyjmpoBKe TeopeuH anaic ctffl} odoaHaiaei cieneHB (B ecie -CTBBHHOM cuHcae) ajieueHia /7 Kontaa ft (CM. § 2 n. 2).

MOKHO nociaBHTB aaaaiy o <3 o n / c a n n H K Ji a c c aK o ^ e a , K O T O p u e H B U H B T C H a j i r e f i p a u n c^ H a s £> c c H C i e u o a o d p a a y n n H X /-\

U H O x e c T B o u o n p e a e ^ H i o m H x c o o T H o m e -H H fi (3), r a e Wd-;/?,-, ui>:fLe ^ , H a Ji H K o T o -p H X B H I I O J I H H e T C f l $ a K T O p H 3 a a H O H H a H

T e o p e u a B.OcHOBHoK iiejiBB HacTOHieH padora HBnfleiCH pemeHHe nociasjieH »

HOB Btrae saaayn npw cjieayioinHx aonojiEHTejiBHiix orpaiwqeHHHX Ha CH-cooTHomeHHfl (3):

82) Cjiosa X-/ft , ^//t- , i><^I * nonapHO paaraiEH Meawy co -dott.

OCHOBHOR pesyjiLiai padoTH MOSHO c$opHynHpoBaT£ cjiesyjonum oo-pasoM: K n a c c a n r e o p c y H a s J? , K O T O -p u e s a a a H H co o x H o m e H H H M H (3), y a oB J l e T B O p H D m H M H y C J I O B H H M S I ) H 82), H B

K O T O P U X B l i n O J I H H e T C H $ a K T O p H 3 a i ! H

o H H a H T e o p e u a B , c o B n a a a e T c K Ji a c-c o H 5/V - K o n e ij (CM. § 2).

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HBJIHBTCH aJiredpaMH c I, aaflaHHHUH neKOTopoH CHCXSMOR oopaaymmnxt"\ OnpeaeJIHBlMUH COOTHOmeHWHMH BHaa (3). IIpH 3TOM COOTHOme -

HHfl (3) SOJI2CHH yXOBJieTBOpflTB, KpOM6 yCJIOBHB SI) B S2), 61116

HeKOTOpoMy ycJioBHio S3) (CM. onpe^eJieHHe I), Koiopoe BapaiaeTipedosaHHe "HecyiwHpyeMocTH" cooiHomeHHl! (3). Ho onpefleneHHD.cso-

ajiredpa OTHOCHTCH K qacay S^/V -Koneq. flajiee, asB § 2 Teopewu I cjieayei, qio nopMaJiBHiie am-edpu B

A.H.MajiBiieBa [3] , [*] , cooTBeicTByroipe HOpManLmoi cucieMaH pa-B6HCTB des neBicc, npasux a cpeaHHHbK UHIUIOB %mmi 2 (CM. § 2, n.3), a TaKJte ajiredpH/^y,??^^ HS padora asTopa [5] npHHaaneKar KKJiaccy SN -KOJieu.

B KOHue § 2 aaeTCH onncaHne scex cooTHomeHHti BH^a (I) ZJIKOflHOpOflHHX 3JieM6HTOB ^B^CfJ) JIBdOFO SN -KOJIBIja.

B § 3 flOKasuBaeicfl ocHOBHaa TeopeMa padoiH (TeopeMa 3), KO-Topan yiBepacaaeT, ^TO B S/V -KonBijax BunojrafleiCH $aKTopH3aipi -

TeopeMa B. OdpaiHoe yTBeps^emie o TOM, vro ycjiosae

28 JL.A.EoKyiB

cneacTBHeu ycjioBHtt 81), 82) H TeopeuH B, noqia oie-BHflHO.

B § 4 yciaHaBJiHBaDTCH HeKotopae cjieacTBHH reopens 3. HiteHHO,aoicasHBaeTCfl, mo S/Y -Kojn>n.a yaoBneTBopjnoi ycnosrao e a H H -C T B e H H O C T H s o n o j i H e H H H (leopeua 4 ) . Oicioaa

(cjieacTBHe I), iTO B <5yy -KojiBijax BtraojiHHeTCH cseay-

jnodHX HeHyaeBHX aaeueHTOB ^ o HS S// -KOJisqa /? cy-TaKHe anew en TH c H o^ , ?TO

a f t n 6 f t = cftj Hana-g=ftd. , (S)

rje, Hanpmiep, a.R- rjiaBHHfl npaBHit Haean, nopoaweHHHii

Kojrtiia ($ea aeJiMTeJieil Hyjw H o 1 , yaoBJieTBOpnioiime(5), HaasaHH Haua B pafioie [5] £?/? -KOTOEtaira ( gwazi Bezout )

•). Kmcc QB -KOJieu HBaneTCH Cojiee mHpoKrai, qeii KJiacca Be-sy-KOjueu H WB -ROJICU ( weak Bezout rings ) , paccuaxpHBasnuiecHKOHOM B padoie [6} . KiieHHO, Beay-KOJiBua, Kpoue ycjiQBMft (4), yao-BJIOTBOpHBT eme yCJIOBHB

aft +

a B V/B -Kojimax npeanaymee paseHCTBo BunojiHHeTCH Becra a.ftn£R.*O.

KB nocJieflHHX pesyjiiiaTOB, BBHay Toro, ^TO cymecTByri 3/V -Koxbiia, He BJiosmiue B TeJia, noayqaen yrBepsgeHne:

CynecTByBi Q 3 -KOJima, He BJiosrauie B lena.OTM6THM, ITO Eesy-KOjiBua yaoBJieTBOpiroT ycJIOBfflo Op9 u nosTOiiy

BJIOSHUH B TeJia ( [6] , ieopeMa3.3). flnfl W3-KOJieu sonpoc o<5 meBflOKHMOCTH B T6Jia OCTaeTCH OTEpUTUM.

B KOHue § 4 (n. 3) noKasHsaeTCH, KHK H3 xeopeuu A$aKTOpH3ai(HOHHafl Teopeua Kona ann KOJICU co cjiadm

OTMeTHii, q?o c noMonttB pesyjiiTaTOB 3ToM patiora UOHCT CursoCo<5^eHO ocHOBHoe yTsepsaenHe pafioiH asiopa [5] .HUSHHO, ecjw 5 -noayrpynna c I i co CTeneHHOB $yHKunefi d(oz) (c OOIWHMIH CBOfl-ciBaMM :d&)=q> -f, 2 _ , . . . ; d(x) = O TOJIBKO npa x= /, d.(ja/)=c(£x:)-t- ctfy))*TO B rpynnoBOM KOJiti^e P^Sj , rae P -nojie, MOKHO paccMOTpeiBMHOieCTBO OflHOpOSHHX 3Jiei«eHTOB

77

S , of (Srj = y J / ^ - V ~ n

ae aueei aejiaiejiea Hynn, TO aio unoaecTBO oOpaayeinoayrpynny no yuHoaeHHB.KOTOpyB MH Cyaew o<3o3Ha^aiB qepes

$aKiopn3aiyioHHue leopeuti ZUIH HBKOTOPHX KJiaccosKOJieu. dea aeJiareJiefl HynH. I.

Ododman saaaiy, nociaBjieHHyio B [5], MOKHO yicasaiBsapaaHT npodaeMH Majimesa, o KOTOpofi rosopHJiocB B [5];

CymecTByei JIH KOJIBU.O sa^a P(S) , rae S - nojiyrpyraia cocieneHHoft $yHKn.Heft , TaKan, ITO:

1) P(S) des aejiHTeJiefl Hyjin;2) P(.S)hcrm BJiosmia B rpyunyj3) P(S) B Tejio He BJioaraio.OKasusaeTCH ( a STO ycTanaB^HBaeTCH c noiiomBD pesyjiBiaiOB

aroK pafioTu), TOO raicae KOJiBi^a cymeciByioT H iro TaKHMH dyayi, na-npawep, KOJIB^a P(Qn), n> 3 , nocTpoeHHHe asTopoM (CM. [5] ).

§ 2. SN -KOJiBua

1. B STOW naparpa$e uu npHBeaew onpeseJieaHe S/V -KOJICU HaoKaaeM asa yTBepaseKHH, oaHo as Koiopttx npeaciaBJiHeT co6oii ao -CTaioiHoe ycjioBue npHaaflJieKHOCTH KOJiBi^a K^accy S/Y -KOJieij.

2. IlyciB S - nojiyrpyraia c I, savannas B HeKoiopOM

AL =BL (eel), (6)yCJIOBHHM:

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i 5 ^^/} H6 HBJIfleiCH KOHeiHOa <5yKBOft flJIfl

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napno pasjiH^HH ueny codod.ycjioBHMCH B KaieciBe MHOKecisa I sonycKaiB H nycioe

BO.3a$nKCHpyey TenepB Jiesue H npasue yacTH pasencTB (6). CJIOBO

X aj[$aBHia /^ dyaeii HastiBaTB KaHOHMiecKim, ecrai OHO He co-flepKHT B KaieciBe noac^os HH OHHO HB CJIOB /7t- . OdosHaqaii qe -pes n COBOKynHOCTB scex CJIOB nojiyrpynna S BKJiBiaH H I ,HMe-

KaHOHnyecKHfi BIW. B cmiy leopeuu HeJliiaH ( [7] ; CM. [5], § 2 ), qio SJIH paccMaipuBaeuoa nojiyrpynnn S Ka^oe CJIOBO an-

pasHo Oflnowy H TOJIBKO oflHouy cjiosy MS MHOKecisa /7 .IlyciB TenepB P - noae, PC$) - noayrpynnosaH aaredpa c I

noayrpyraiH S naa nojcu P . OnpeaeJiHii B anredpe P(S) $yHKiuiBCTeneHH d(X) , X&P(S) . HiieHHO, cieneHBB cjiosa naaoseM eroflMHy. IloJioacHU npw SXOM, yio d(d) — O . OflHopoamojCTeneHH 77 HasoseM nHHeHHyn ROHdHHaiimo CJIOB S^HHBI n HJIHECJM TenepB X^PCS; H

30 Jl.A.BoKyiB

^ - oflHopoflHHie 3JieMeHiu cieneHM , ^^O, TO nojiosuni ,aL(X)-&- • BJieMeHT Xd B flajiBHeftmeM dyaeM HasusaTB ciapmea

BJieMeHTa X H odosHatjaiB X^ = X .HocTpoHM Teneps, HCXOTIH MS cHcieMH cooTHomeHHfi (6),HeKOTOpyw

cucTeuy paseHCTB ̂ . HueHHo, nyciB HJIH aeKOTOporo t

W}h}u,-f€. +* . Torsa B cnpaseanHBO paseHCTBo:

(8)

HOB ̂ uu CyaeM noHHMaT£ coBOKynnociB BceBosuoKHbix paB6HCTB (8), nOCTpOeHHHX flJIH BC6X L €. J '.

PaccMOTprai Tenepi. cneayiomee ycjiosHe:/f^BjCjJ)- HenyjieBbie osnopo^HHe

P(S) H

(9)Toraa 3TO paseHCTBo HMeeT OBHH HS cneaymmax BUZIOB

1) £=/7X, 8=XD, X^P(S) ,

2) fl

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fl,B,C,Q cieneHH I.MOXHO cKaaaiB, ITO ycjiOBMe (10) BupaacaeT

MCXOHHOii CHCTeMbI COOTHOineHHK (6).

OIIPEIEJIEHME I. S/V -KO^BUOM Hasosew KOJIEH.O saaa P(S) ,yso-ycjioBUHM so) - S3).

SAME^HKE. Cpasy BHSHO, ITO K uacjiy SJY -KOJICU OTHOCHTCHajiredpti, TaK Kan ycjioBHH (7) H (9.2) B STOM cjiyqae HH -

ijero He supaKaioT, a ycjiosne (9.1) JIJIH 3neM6HTOB cieneHH IHO.

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flJiHHti 2 (B qacTHOCTH, IJHKJIOB anHHH I). AHaJiorH^HO noHiuiaeTCHycjiosae a^H npasux M cpeflHHX lynoios HJIMHH 2. (noa cpeflHHHMi

rpa$oii Mbi dy^eu HOHUMSTB rpa$, BepiiiHHauH Koioporo HBJIHIOTCH see

<DaKTOpn3amioHHHe TeopeiiH<5es

HeKoiopux KJiaccosHyjin. I. 31

H Bee KOHeiHH.e fiyKBH CJIOB cacTeiiH (6) a ase dyKBu or,£KOTOporo coeflHHeHU CTOJIBKMMH pedpawH, CKOJIBKO pas B (6) BCTpeia»-TCfl COOTHOmeHHH

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2) IlyCTl Wh = Uf - H6KOTOpO£ COOTHOffleHMe H3 (6),

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Toraa oaHO HS cnos

HBJIH6TCH yCTOflqHBHM flJIH CHCT6UH (6).

SaueiHU, ITO ycjioBMe (II. I) HBJifleTCfl HeodxoaHMHMnesHocTH ajirefipbi P(S) K KJiaccy S/V -Konei^.

TEOPEMA I . E C J I H C H C i e w a c o o T H o r a e H H J l( 6 ) n o n y r p y n n u y f l O B J i e i B o p f l e i y c j i o -B a H u (7) H (II), TO a j i r e d p a P (S} , r a &P - n o-j i e , n p M H a s J i e K H T K K J i a c c y 5/V - a Ji r e d p.

- HeKOTOpuft BJieweHT ajiretfpHJOKA3ATEJIBCTBO. Dyci*

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Kpoiie Toro, B 3ioa se cjiy^ae SJIH jaofioro /7^ MU dyaeu7^ e/7 .PaccuoTpHii lenept B ajiredpc P(S) paseHCTBO

32 J.A.EoKyiB

B, C, 3) - HeHyjieBHe oaaopoflHue sJieiaeHTH cieneHu I ,nKaaceu, ITO axo paseHCTBO mieeT BHJ (9). floKasaieJiBCTBO dyseu sec-TH HHflyicmiea no iHcay n(fl) + n(C). "&S3as.7i(fl)-f-7i(C)-2^.s.ti(fl)== n(c)=di TO name yrBepsaeHHe OIGBHSHO BBHBJ ycoioBHH (II.I).

IlyeTB TenepB rz(r/7)*-77(£J=/<>2. . PaccuoipHM asa cjiyqaH.I) /?3Vv; 2? 9,6 H CJIOBO W/i Hueei ce<5e nojodHoe B Jtesofl

paseHca?Ba (12). Toraa cymecTByDi TaKHe Uf f €. ̂, & 3f H W£ = ^/y - OSHO us oooTHoraeHHfii (6).z^A , cTOHmae B Jiesofi qaciH paseHCTBa (12), B cray yc-(II. 2) HBJMBTCH yCTOfl*fflBHMH. 003TOMy C3W, U ,%3-f, h. Ec-

JIH reneps /^3^r , TO OHHTB B cajiy (II. 2) nojiyjaeu, «JTO O^HO usCJIOB Xf, JT/? HB3IH6TCH yCTOaTOBIflJ H nO^TOMy C 3 3C. . 3lO HO-

KasuBaei, yio see <5yKBU, ExoanmHe B /^ , EXOBHI H B £

B paseHCTse

#(B - a '4 '£} =(c- d'40)£ (13)

C-a &fl nueeT MeHBiiiyn Bacoiy, yew sjieueHT C . Ho npea-paseHCTBo (13) Hueei sna (9). Ho Toraa H

Hoe paseHCTBo (II) HMeei BHJ (9).2) IlycTB TenepB HHicaKHe asa CJIOBB us JiesoK waciM paBeaciBa

(12) He noaoSHH uescay cofioft. B CHJiy CHMiieTpHM, 310 KB MOKHO npea-HOJIOKMTB H SJIH cjioB npsBofl qacTH pascHCTBa (12). flaJiee, ec^M see<5yKBH, Bxoafliiwe B fl , BXO^HT H B C , TO paccywaeHHH npeHtwyme-ro cjiywaH noKasuBaioT , ITO (12) nueeT HeodxoflHMbiii BH^. tloaTouy MO-KHO ciHTaiB, yio B /7 BXOSHT O'yKBa, ne BxoflHman B ^ , a B C

(5yKBa, ne Bxoaninafl B /7 .HaJiee, BCJIH n(B)= 77 (&)=*.!, TO Haiiie yTBepacaeHiie JierKo CJIG-H3 (II.I). IIosTouy MoacHO CIHTSTB, WTO B^h,}h2 V(.h^^h2.

IlyciB W - (SyKsa, BxosnmaH B fl , HO He BxoflHman B C . Tor^aC?",, "z ,•V/h^u.f, ,

OflHO MS CJIOB U,fz ,UZ-/, , B CHJiy (II. 2), HB^fleTCHBHU. IlycTB, aanpmiep, lamai dyaes CJIQBO ^/y^B CHxy (II. 2) H Hamiix npejnojioxeHHlt , CHOBO wy2 * sxc^Hniee B jiesyio qaciB paBeHcisa (12), He HMCBT cede noaodHtix cpesa CJIOB as

TeopeMH JJIH HeKOTopux KJiaccos6e3 aejiHiejieK nyjiH. I .

33

(12). STO noKastisaeT, ITO paccMaTpHBaewHftTeopeua ^OKasaaa.Jlerico nposepHTB, ITO ycJiOBHHW sioft TeopewH ysoBJieTBOpjnoi HO-

piaajiBHHe ajireCpn A.M.MajiBueBa, cooTBeTCTByromHe HOpMaJiiHuiiuaw paseHCTB, ne coaepsamuM Jiesux, npasux, cpeflHHHHx L^MIUIOBHU 2. Kpowe Toro, ycjioBHaw 3ioti Teopewu yaoBJieiBopHioT

, H3 (5).*. floKaseu saeci HeKoiopae yTBepaaeHMH oTHocHTe^BHO » - KO-

JIEMMA I . S / V - K O f l i i j a n e c o a e p a c a T ae n e f l n y j i H .

ZIOKASATEJIBCTBO. npeanoJiosnu npoiHBHoe. IlyciB

. Monou B - oflHopoflHbie ajieueHTH. IlyciB /7 s> /70 , /7=XaHbie ajieueHTH. IlyciB /

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paseHCTBO.y = o , T.e.

Jf tfftO, 8,* O- JlersoBO npOTHBOpeiHT yCJIOBHHU (7), (10).

STO paseHCT-

JIEMMA 2. II y c T B Be i C H p a s e H C T B O

- K o Ji B K e P(S) M M e -

(15)

r a e ^ ^ - H e H y n e B i i e o a H o p o f l H H e 3 J i eu e H T U c i e n e H M 1 , ^ ^ - H e H y n e B u e o f l Hp o s H i i e a j i e u e H T U c i e n e H H 7 ? / 7 ? > ^ . T o rs a p a s e H C T B O (15) M M e e i B H J (9).

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^hjeT** ' ft aJieiieHTu HS hj Bj , hH B k npwHe noflofiHH apyr spyry. KpoMe Toro, ciHiaeM, ITO

(cooTBeTCTBCHHO, HI ) nonapHoPaccMOTpMM coBOKynaociB scex CJIOB

VVt-/? I^L^Tn /4jnp (16)

34 JI.A.EoKyTB

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(22)

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36 JLA.EotcyTB

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(23)

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37

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38 JI.A.EoKyiB

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(51)

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(35)

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(48)

44 H.A.EoKyrs

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(50)

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48 JI.A.EoicyTB

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(62)

Bcex ajieueHTOB 6,2) , ysoBJieTBOpnioiptx pasencTBy (62), BH-depew aneueHTH .5*2)* , ann KOTOPHX TOCJIO

50 JI.A.EoKyrL

npHHHMae? MHHnuajii>HoeIlpHMeHHM K npOHSBOJIBHOMy H3 paBBHCTB (62) H paBCHCTBy ft B =

=C.Z)*TeopeMy 4. Toraa nojiyyuw, ITO

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9io

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STO yiBepsaeHHe BtiieKaei MS npefli«p;ero B cmiy ioro $aKia ,ITO cymecTByBT S/V -KOjaija, ne BJioauoiHe B iena.

3. B STOW nyracie UH noKaxeu, KBK us TeopeMH fl cnegyeT $an-Teopeua Koaa \_2\H KOJiea co cjia<5mi ajiropHTMOM.

, npeKae scero, ^pHHaz^JIeKa^ee Kony [2} onpeaeaeraieKOHTHHyaHTHHX IIOJIHHOMOB. IlyCTB t,t ti) . . . - HeHBBeCTHite.

fM- • • ̂ =fn-i (t, -..t^trSfn-zfr...^) (63)

B-pacSoie 2 aoKaaaHH c^eayiomiie paseHCTBa:

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B cmiy Teopewa /^ tieisepKa (tf,B,C,1))i cooTBeTCTByomafl

TeopeiiH BJIH HeKOTOpnx KJiaccos($63 seaHTejieft HyjiH. I.

51

paseHCTBy (64), nonyiaeTCH us ajiejiema (X,/,j(,i)c noiiomw) onepa -mitt /), /^y , </>x .

PasencTBa ^-jf = / • / uaieaT BBS C6'0 o /z.= ^? . flanee, ecjm KpaseHCTBy (66) BHaa (67) npHMeHHTL onepaiyiH p ana fa y ,TO nojiy-

paseHCTBO TOPO xe

(67).Toraa

, 3,6,0,7)

'C, =-

HaKOHea.paccuoTprai paseHCiBo

Toraa

X y

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B17.17.1965 r.

I. Cohn P.M.

2. Cohn P.M.

3. A.E.

A.M.

J l H i e p a i y p a

Factorization of in non-commutative powerseries rings.-Proc.Cam.Philos.Soc., 58(1962),452-464.

Rings with & weak algorithm. — Trans.Amer.Math.Soc.,109 (1963),332-356.

accouMaiHBHba CHCT6U B rpyniui -Mai. C(5. 6 (1939), 2, 231-336.

0 BKjnoieHZH accoiinaTHBHux cHCieii B rpyium II ,—Mai. c<3. 8 (I9*0>., 2, 251-264.

52 JI.A.BoKyTB

5. BoKyTB JI.A,

6. Cohn P.M.

HeKOTOpne npnuepu xoneu, 6esH JiorMKa, 3 (1964), 5-6, 5-28.

Noncommutative unique factor! eation domains.—Trans. lmer.Math.Soc., 109 (1963), 313-331.

7. Neumann H.

8. ASHH C.H.

On theories with a combinatorial definiti-on of "equivalense".- Ann. of Math. , (43(19^2)223-243.

0 BJioiBHra nojiyrpynn B rpynnH.— 3AH(I960), K> 2, 255-257.