ajiteepahjiorhka tou 4 bunyck 4 pykoboahiejii …math.nsc.ru/~alglog/01-10/04/04n4-2.pdf ·...
Post on 16-Feb-2019
212 Views
Preview:
TRANSCRIPT
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).
PaccMOTpnu dojiee nospodno cosepsaHHe Haciosmei} padoxu.B § 2 aaeiCH onpeaeneHHe SN -KOJieu. KoJIB^a KJiacca 5yV
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:
"SO)51) HHKaKan HaqaJiBHan dyKsa JJIH CJIOB UHoacecTBa
i 5 ^^/} H6 HBJIfleiCH KOHeiHOa <5yKBOft flJIfl
CJIOB aToro se uHomecTBa;52) Bee CJIOBB, sxossipie B cooTHOineHHn (6), no-
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) $yHKiuiBCTeneHH d(X) , X&P(S) . HiieHHO, cieneHBB cjiosa naaoseM eroflMHy. IloJioacHU npw SXOM, yio d(d) — O . OflHopoamojCTeneHH 77 HasoseM nHHeHHyn ROHdHHaiimo CJIOB S^HHBI n HJIHECJM TenepB X^PCS; H
30 Jl.A.BoKyiB
^ - oflHopoflHHie 3JieMeHiu cieneHM , ^^O, TO nojiosuni ,aL(X)-&- • BJieMeHT Xd B flajiBHeftmeM dyaeM HasusaTB ciapmea
BJieMeHTa X H odosHatjaiB X^ = X .HocTpoHM Teneps, HCXOTIH MS cHcieMH cooTHomeHHfi (6),HeKOTOpyw
cucTeuy paseHCTB ̂ . HueHHo, nyciB HJIH aeKOTOporo t
W}h}u,-f€. +* . Torsa B cnpaseanHBO paseHCTBo:
(8)
HOB ̂ uu CyaeM noHHMaT£ coBOKynnociB BceBosuoKHbix paB6HCTB (8), nOCTpOeHHHX flJIH BC6X L €. J '.
PaccMOTprai Tenepi. cneayiomee ycjiosHe:/f^BjCjJ)- HenyjieBbie osnopo^HHe
P(S) H
(9)Toraa 3TO paseHCTBo HMeeT OBHH HS cneaymmax BUZIOB
1) £=/7X, 8=XD, X^P(S) ,
2) fl
TenepB Ha KOJII.UO P(S) cJieflyiD«ee ipedosaHHe:S3) ycSOBHe (9) BHnO^HHeTCH flJIfl BCeX
fl,B,C,Q cieneHH I.MOXHO cKaaaiB, ITO ycjiOBMe (10) BupaacaeT
MCXOHHOii CHCTeMbI COOTHOineHHK (6).
OIIPEIEJIEHME I. S/V -KO^BUOM Hasosew KOJIEH.O saaa P(S) ,yso-ycjioBUHM so) - S3).
SAME^HKE. Cpasy BHSHO, ITO K uacjiy SJY -KOJICU OTHOCHTCHajiredpti, TaK Kan ycjioBHH (7) H (9.2) B STOM cjiyqae HH -
ijero He supaKaioT, a ycjiosne (9.1) JIJIH 3neM6HTOB cieneHH IHO.
Bseaeu neKOTOpue aonojiHMTejiBHue onpeaeJieHMH. Byaew TOBOPHTB,ITO CHCTeua cooTHomeHHa (6) He coaepatHT nesicc UHKJIOB SJIHHU 2, ec-JIH sesHK rpa$ aioK CKCTeiiu cooTHoineHHft [8] He coaepKHi jiesax UHK-
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
aajiee, CJIOBO ^JIHHU 2 ycToaqHBtai, BCJIH OHO He BxoflHT BCHCTeiay paseHCTB (6) B Kaqecise Jiesofl HJIH npasoa qacieft.
IIpesnojioEiui TenepB, ITO Hcxoanafl cHcieMa cooTHOineHn8(6)nony-rpynnu S yaoBJieTBopHei ycjiosHjai:
1) CHCTeua (6) He coaepacHT jieBtix,npaBbK, cpeflHHHtixUHKJIOB flJIHHH 2;
2) IlyCTl Wh = Uf - H6KOTOpO£ COOTHOffleHMe H3 (6),
x - HeKOTOpan <3yKBa aji$aBHia " t . Toraa OflHO asCJIOB 3:̂ -2T/" HBJIH6TCH yCTOftqHBHU flJIH CHCT6MH (6).
3) IlycTi HMeew flsa paaM^Hhoc paseHCTBa HB (6)
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*
/7t e /7 . tocjio A , yiacTByxHuee B BTOMBe, (5yaeM HasusaTB B H c o T o ft aJieueHia /7 K ofiosHaqaiBpes
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 /
ar,<f6^] . CoCepeu B paBeHCTse (14) seeco cjiosa X H OKanqHsaioipecH Ha CJIOBO
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).
flOKASATEJILCTBO. IIpeacTaBHu aneiyieHTH /7 H ^ us(15) B
^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
H soicaaeM, UTO XOTH 6u O^HO HS STHX CJIOB Wi0hj0 He Hweei ceCSenoaodabix cpeflu ocTajiBaux. fleiicTBHTeJiBHO, nyciB, aanprcuep, 777 £/o.PaCCMOTpHM CJIOBa
EOJIH see OHM HMeroT noflodaue cpeflw CJIOB V/ihjj i^i , TO, TaK KBKCHCTewa COOTH01U6HH0 (6) H6 COSepSCHT JieBbtX IJHKJIQB JflHHH 2, 1JH flOJl-
KHU filiflH dbl HMeTB, 1TO 77?-/>/7 , TO 6CTB TTJ^p+d t 1TO H6B03 -
MOKHO.
MiaK, nyciB CJIOBO Vv^^ ne Mweei cede noaodHHx cpe^H ocTajiBHHX CJIOB as (16). CodepeM B Jiesoft a npasoa lacinx paBeaciBa (16)cjiosa, HaqnaaiouuiecH co CJIOB, paBHHx cjiosy W,/i/
Bah, 8', C3W,h,C'
B--Q,Toraa MMeei Mecio paseHCTBO
a?)npjmeu BunoJIHfleTCH cooTHOiuemie
, ITO ecjiH paseHCTBO (17) HMeei BIW (9), TO H acxoaHoe paseHCTBO mieei BH^ (9).
aeMMBi 2 TenepB Jierno BHBeciH m npeannyntHx, HcnojiBsyn HHayKmno no BHCOTC n(B} 3JieueHTa 3 .
Jleuua 2 flOKasaaa.TEOPEMA 2. II y c T B B 5/Y - K o Ji B u e P(S) u u e
e i u e c T o p a s e H C T B O(18)
~ n P ° H 3 B ° fl B H H e H e H y j i e s n eo a H o p o f l H u e a j i e n e H T H , ct(fl)^c((C) . T o r a aB I O p a s e H C T B o a w e e i B H H (9).
flOKASATEJILCTBO Oyaeu BBCTH HHflyKimefl no nape
, TITO SIM napu ynopjmoieHH jieKCHKorpa^H^ecKH a ^TO BO scexpaseacTsax (18) $uKCnpoBaau Jiesue u npasue uacTH. .
ct(/7)-Ji cf(3))=J , TO BBiwy JieuiiH 2. IlyciB
(<*(*) ,<*&})-(*,£)>(*,*) . (19)
PaccMOTpHii MaoffiecTso Bcex pasencTB (18), ysoBjieTBOpHiomHx yC
$aKTOpH3amioHHue Teopeuu fljrn HOKOTOPUX KJiaccos 35(5e3 seJiHiejieM Hynn. I.
JIOBHIO (19), H flOKaxeM c noMomwo . HHayKUHH no iHcay n(fl)+n(C)i1TO OHH HM6DT BHfl (9).
77fCJ=3. , TO yisepsaeHHe, KBK aerKO BnaeTL,cnpa-(CM., aanpHuep, aajEbHeflmiie paccyaaeHHfl) .
IlyciB /7 ̂ /^0 /7, =X, W , rae W - Cyras. PaccMOTpmi B Jie-H npasoft qacTHx paseKCTBa (18) see cjiosa, Hawiuiaioiptecfl Ha X, .
, (20)
(21)
rfleB CHJiy npeanoBoaeHna HHayKiwa nojiy^aeu, 110 paseHCTBa (21)
HM8DT BH« (9),6CJIH TOJIBKO /^ ̂ (9, <^ +O .flpM 3TOU OHH
HO HM6IOT BHfl njf(50 (9.1) C OflHHM H T6M K6 3JI6M6HTOM A ; JIH(50
(9.2) C OflHHM H T6M «6 paB6HCTBOM \/M = U.F €•??£. . 9lO IIOKa -
3biBaeT, qio pasencTBO (18) B pacciiaTpHBaeMOH c;iy<iae nueei BHA (9)TeopeMa 2 aoKaaaaa.SoKasaHHoe yiBepsaeHHe npe^cTasjiseT coc5ofl
leopeuy SJIH nojiyrpynmi osHopoflHia ajieueHTOB SN -
§ 3. QaKTOpHsauMOHHaH reopeua ann 5/V -
I. IlyCTB P(S) - HCKOTOpOe S/V -KOJIBUO. PaCCMOTpHM COBO -
Z scex qeTBepOK (/7fBjC,&) HeHyjueBic 3JieMeHioB KO^B-T3KHX, 1TO B 9TOM K03IBI16 BHHOJIHfleTOfl COOTHOieHHe
(22)
Hepea /V ofioaaaiHU no^MHOxecTBo H3 fflZ, , cocTOflqee uscooTBeTCTBynmnx HCXOSHHU cooTHomeHHjai (6). BKJDOIHM B 3?oCTBO H qeisepKy
HueeiTEOPEMA 3. (^aRTopHsaqaoRaafl TeopeHa SJIH 5/V -
n p o H S B O ^ B H i i K a 01 e u e H T u H o a e c i s aU O X B O n O ^ y i H T B H 3 d J i e i i e R T O B M H O
a c e c T s a / y c n o M o m s B c j r e ^ y i o m H x o n e -p a K H it :
36 JLA.EotcyTB
3)fa (ft, 8, C-2J =
cL(fl + CX) 2 d(fl), d(XB-<#) 2
SAME^AHHE. JlerKO HOHHTB, ITO ecjia B(7), BHnOJIHH6TCfl C$OpMyJIHpOBaHH
peim, TO 3To KOJIBUO yflOBJieTBopnei ycjioBHn (10). B aiou cuiicjie yc-JIOBM6 (IQ) HBBH6TCH H6 TOJILKO flOCiaTOqHHU flJIfl BbOIOJIHHUOCTH T60pe-
MH 3, HO H HeodXOAHMUM.
2. ycjioBHMCH o<5 oflHOM ocJosHayeHHH. HH36HCH y <5yKB <3yayi os -mo paccwaTpHBaioTCfl OflHopoflHae 3Jie»ieHTH ynaaaHHoa cieneHH
Hyjiesue sjieiieHTu. HojioacHM, Kpoue Tore, MTO BHpaaceHHH,i, odoaHaqaioT HVJIB KOjiBita PCS) .
3. Teopeuy 3 dyaeu TiOKasuBaiB c noiiomBJO HHflyitaHH no
(23)
ECJIH TOIlyciB // ^ 2. . HpMpaBHHBaH B (22) HaHdonBineH cie-
neHH,
= C£> .
, nanpHuep, /? - ciapiaaH laciB aneMeaiaMti 2, paBeHCTBO (24) jaueer BUS (_9). IlyciB(9.1) H, Hanpnuep, fi = CX , ^=X^ . Toraa,cooiHomeHHe
. B cajiy reopeOHO nwees
, ITO Gf(/7 -CX)<tfp?)j d(£-XB)<c((2))nojiyqaeii HeodxoaHMoe nait
nycTB TenepB RXR cooiHomeHHH (22) paseHCTBO (24) HMeeT(9.2). B cany onepaimH _fa B <^ MOKHO ciHiaiB,d , yiacTByBnmfi B paseHcrae (9.2), paBen I, a
6CTB OflHO US HCXO^HiCC P3B6HCTB (6).
Ilocjie 9THX npe^nojioKeHHii paseHCTBO (24) npaueT(25)
B paccuaipHBaeMOM cjiyiae MU mieeu, iro dffl) =
QaKTopasamiOHHHe reopens BJIH aeKOToptcc luiaccosdes aeJuneJiefl Hyjifl. I.
37
rae #;l£±,&i,Q^ cooTseTCTBHH c IIPJIHHTHMH o<5o3HaqeHMHMH,ecTi.BJieueHTH cieneHH / HJIH HyjM.
CpasHMBan B paseHCTse (22) sjieMenra o^Hofl n TOM %e cieneHH ,cHcieiiy psseHCTB:
'777 , (26-
IIpH k<O paseHCTBa (26. k ) mienisa (26. 77V-77Z) no JCJIOBIHO nojiyiaew:
paseHCT-
*j(tyfyXj/)eM. Mcnojitsya nocjieanae paseH-, nepenameu (26.77+777-1) B saae
<.)Wm_, • (27)
(27) ecTL cooTHOiiieHHeOHO H6 MOS6T HM6TB BHfl8 (9.2) . II03TOMy
O^HOPO^HUMH 3JieM6HTaMH.
rje cf(X) = d .Ilpa X *= <? 3TOTdHHaqnett KEK ROHeqHitx, TSK aHO 3TO H6B03MOZHO.
otfpasoM, as paseHCTsa (25) nojiyiaeu:
dun OH JiMHeflHOfl KOII-6yKB oooTHoraeHHtt (3).
=?n-<f • (28)
IIo npeflndJioxeHaB, nz 1, 7712.4 . IlycTB, HanpHMep, n=l . Tor-paseHcrao noKasusaeT, ?TO x . = C_ =O .
38 JI.A.EoKyiB
oCpasou, paseHCTBO (22) aueeT
sioro fiyaeu c^maTB, qio n~>-f} rn'>1Ms pasencTB (28), BBHay Teopewa 2, joieeu:
a , ̂ _̂x =/
_ a =6> HJIH ^^-2 = 0 HePaccMOTpuM TenepB TaKoe uaKCHwajiBHOe IMCJIO A, , npn KOiopou
HM6IOT M6CTO
Bcex 1 £i *i K, .Ms npeflbmymero BHSHO, ITO k,^ 2. . Byaeii CTOTBTL , ITO
kt<7Z+4 HJIH A", < 77? +1 , TaK K3K MHaie paB6HCTBO (22) HM6JIO 0H
BHfl (9.2).
BbincuiHeHHe paseHCTB (29) ofiecneqwBaeT BimojiHeHne nepsHX &/paseHCTB CHCTeMH (26) : ( 26. n + m ) - ( 26 .n+Tn-K,* 1 ).fleB-CTBMT6JIBHO, paB6HCTBO (26. 71+7T7-S ) t TflO O^= S ^ /</-/ , B CHJIJ
(29) BHnojiHfleicfl noqjieHHo (TO ecit nepstiB IJIBH Jiesofi ^acra paseHnepsouy qjieay npasog H T.a.).
PacewoTpuM paseHCTBO
CK)fla SHaieHHH /7 '̂ '̂ , B3HTH6 H3 paB6HCTB (29), HO-
)rn= O .H Q MS (29), (5yae«
/?n^f,*JWfn., . (30)
MaKcwuajiBHocTH /rx , nocjieflHee cooTHOineHHe ecT& cooTHomeHHeHeHyjiesuiiK aneueHTaitM. II o Teopewe 2 OHO EOJISHO MMOTB
(9.1). IIoaTouy
(51)
TenepB, wo as oooTHoaeHHft (26. n+7n-~/<, ) -(26. 77-/-77Z-.2A-, ->••/ ) cjiesyKT
xeopemi BJIH Hexoiopia wiaccoB 39(tea flesHTenefl Hysn. I.
*n-
^^ s ~j£ • nPH -5=^ aiH paseHCiBa y«e flOKasaaH. npeano-JIOXHM, ITO $opMyra (32) sepHH flflH scex aaeudHToa Vf,^ } W^-; *
^6^5 4/fx-/ . flOKameu EC WIH V^^-,/ ^PaccuoTpm paBeHciao (26. 77-^-777-^^-5 ):
-(\*/8f> -
rae o ̂
, rae /? ^ 777 .
CrpynnHpyeii B paseHcrae (33) qaesH Bi^a /7t- Bj M O<^/' •3Toro, McnoflBsyn paseHcisa (29), HH4yKTHBHoe npennonomeHie MKO ITO BseaeHHue odoaHaieHHH, paseHCTBo (33) HOZHO nepeniiean B
(35)
JI.A.BoKyis
- Ot n.-
JlerKo saiieTHTB, wo oCseseHKHe supaaeraiH cooTBeiciBeHHOWOMUOTCH. flaaee, mieei iiecio paseHCTBO
, npa s=ff,-^ OHO oieBHflHo. ECJIH s or, -cray paseHCTB (29) , <&m-K+2 = - - - - &m.-s = O •
CKasaHHoe, as paseHCTaa (35)
B
(36)
, pa-
(37)
= /r,- , TO ecisTeopeiia 2, noayqaeu,
.-K, . ECJIH
(31),B6HCTBO (36) 6CTB paBgHCTBO
XY=ZT ,
.Vj 2, T -
, TO,
rje cL(U,)=i . Ho Toraa ££ eciB oanoBpeMeHHoHaqaaiBHioc dyra cooTHomeHHfl (6) H Koneqioa dyKB STHX coorao-(cu. (34)). BTO HCBOSUOXHO. TaKHM odpasoii, B pacciiaipHBae -
cjiyiae Z=O, Y=0 .nycTL TenepB s<K,-i , TO eciB oL(Z)^ri-K,+i . PaseHCTBo
(36) He uoaei MMOTB BHaa (9.2), TBK KBK OL,L-Kl+i OKUHqHBaeTCHHa KOHeiiwe dyKBu CHCTeim (6). IIoaTouy nojiyiaeu:
z=xu} y=ur.Bo Bcex paccMOTpeHHHX cajnaflx, cymeciByet ajieueHi X K-S-z
(B03MOXHO HyJIi), TSROtt , 1TO
HIf09 ' 0= "X
•ojoi awods 'WHKOICOU •wt£H lorehBHeopo -uv<j/ Hdn *$' Vg^ ' VJ? ' "̂ HHBH8 'OHHaaiOiaaiOOQ "Hlf^H lOlBhBHeopO
* WAX! '
00*
D
' J ' ' BHHasredira soa oih
'( S-zz/+z/'92) BaiOHgaed ojoniifoaenodii en oih 'sdaiiai Jf9KBMOn*(
BMH9Hirouna BEIT onhoieiooK H oiwfoxpcoH (j^) H (6$) aioneaedoih '
:9ffHa a sieojmsdsii OHKOK (6E)BaaoH9aed'BHH9hBH80po Hie
(ot) f-S-^i .. _
-oil o ' '
7-^5- xaoa Hdn(gj) BasoimBd 'noeedpo WKHBI '(6£) if^«do$ oration
= -M
OJ903 8lT
oie
aoooBira XBdoiOHOH Hirff Hriadosi
JI.A.BoKyTi
B BTHX odosHaieanjix cnpaBeflJiHBH cateaynipie
-~><*coo
PaseHCTBo (26. ^ ) UOKHO TenepB nepenHcaTt B BHje:
I riiBj-6+/-/C » 6+
IIOflCTaBJIHH B 3TO paB6HCTBO 3HaieHHfl
BCHCTB (43), nonywoi:• i^j f B8HTH6 H3 pa-
Z dcj3+ i=-K
1+ L = K
cnaraeiiue npasoB a. nesofl ^aciefl »xorb paseBoisa pasra.
. Z K/i Kw ̂ iv^)- Z (^/S-^^"^-"-+>-" rf d*/»K '
SToro paseHCTBo:
(43) mieeu:
__K
*aKTopH3auHOHHHe TeopenH AJU HeKOToracc(tea aejuweaeft Byafl. I.
Tawm ofipasoH, aeotixoAno aoKasaTi paseHcrao
Z V;..,̂ - Z Ot^i V/nl^m.K i ^K
Hcnojn>3yH (4-3), nepemueu npejHayiee paseHCTBO B
-j^t, K-i~s , TO ec» j=K-£tcnpestmymero paBenciBa npmiyi.BHA
. Torsa aesaa H
oc5pasoM, paseHCTBO (45) aonasaHO. Hs aioro paseRCTBa,(44),
9ro H AOKasuBaei paseHCTBa (4i).PaseHCiBa (42) noKasmaDT, wo mieei wee TO cooxaoieme:
tenepi. ajieMeara, B Hcxogaoe eooiBOieHie(22), B Biae:
c -W47)
Ha pasenoTBa (22) B cmiy (46)
(48)
44 H.A.EoKyrs
B nocjiesaeu paseHCTBe cL(V}^cL(Cf~flh} . noKaateii, ITO paseH-CTBO (48) HiieeT
, us (43)
PaseHCTBa (49)flOKaaano, qio wcxoanoe paBeHCiso (22) ecitonepartHH w/i u f) K
Teopeua 3
§ 4. HeKOiopue
I. B alow nyHKie MU flOKaseu neKOTOpoe scnoMoraTejiBHoe yisep-
P(S) - 5 A/ -KOJIBIJO. PaCCMOTpHM B P^ paB6HCTBO
(50)
1) PaseHCTBO (50} ne Hiieei saaa (9.2);2) 3jieMeHra fl,B}C,2) raieioT BHS (25). J
B CHJiy aoKasaiejiBCTBa TeopeMH 3 no;iy?aeii, ITO
' ' 'B',C',2)' - ie xe ajieMeHra, yio H B paseHCTBe (47). B
tJD3MMA 3. I l y c T B H u e e M B K O J i L i t e P(S) p a-
B e H c T B o (50), y a o B J i e i B O p f l u m e e y c j i o B i i -H it (51), H p a s e H C T B O " :
>*-~* (53)
r a e . + O . T o r S a
a e a j r e j i e H T t i Xfl'£' H l e i B e p K a (w,h.,uff) -e a e , I T O H B p a s e H C T B e (52).
3>aKTOpu3aipiOHHHe Teopeuu xnn HeKOTOpiK imaccoB 45des aejiHTCJieii nyjin. I.
flOKASATEJILCTBO. IlyciB
flOKasaTeuBCTBa c$opMyjmpoBaHHoB neioi&i nposeaeu see pacTeopeubi 2 osuoBpeiieHHO .zpin o(5onx paseHCTB (50) a (53).
IIo ycjioBHK nojiy^aeu npesse scero, ITO
fl-Vn-i w, C=V^a 5-/z. U/^./, 2)mieeu
PaccMoipuM IHCJIO /r^ ,- BbifipaHHoe nepea paBeHCTBawH (29) ̂ JIH COOT-HomeHHH (50), H TaKoe ace UHCJIO /r^* , HO cooTBeicTByiomee paBeHCT-sy (53). floKaseM, ITO Kt=Ki* . IIpeanojio3mM, qio K,<K? . TornaB pasencTBe (30) MH raieeM, qio Ot-^. f-tfn-K k=0 a, snaim ^
3io osnaiaei, ITO
paseHCTBa npoTHBOpeiaT sadopy incjia /r/ . 3ioei, ITO /r,=/f (* .
PaseHCTBO (30*), nocipoeHHoe flJifl paseHOTBa (53), HMeei
Oicioaa, KaK joKasaHO,
BIO paBenciBO c paseHCTBaMH (31), MBI, BsnayB KOJitue P($) ,
TenepB, ITO H soodme ajieueHia X f f _ ^ ) . . . > X 0 , $nryB paseHCTBax (52*$ ; nocipoeHHHX arai cooTHomeHHH (53),coB
c aJieaeHTauH XHr2t.--,X0 MS paseHCTB (52).TOB ^_2 H ^-K,-Z uuBHoe npeanoaioaceHHe , ITO
scex I, d-^i^S , rae S^K-1 . flOKaaceu paseHCTBO (55)
• H H B H H 9 H i r O I I O t f H H N H H 9 a X O H M t f 9 0 H H B &
- * ir o H B o x a B i r a B B tt i ir o a - /V5" *
-oaoj n9K£p 01 'jjnaoiroJC xnxe en iraopo i9Bdoax9iraoK£ -y Hirog;XHS9IT HIOOHH9ffIOHHK9 9MffOICO^ BOI9BHHHOU OHhHJOIfBHY
8HHBI
OXh 'I9JCK91TO 'HIH9H9Ife 9HS9ltfH9H - ^ ' ̂ '& *3 'ff ' b
(95) 'ed oxo9R xa9ira y a oxh 'OJQX en Hiro9 'gHHSHironoK XHaedii HXO
anaoico^ x9BdoaaairaoE/ ^/ oxh 'ixHdoaojoiraroa aodoxoH9H -
BaxoH9aBd oaioiirsiBSBHoiz: xgBodgase oxg
oih (ad9ii9x n9BhjCiroii rat t H ^t axongaBd
oxh 'i9^K8iro '(01?) H (62)
OXh 'H9Bh^KOII * 8 f ) HItBaXOH9aBd 0
BaxoHaasd EH H HBH
19-9HH fBHH93EOIfOnK9dn OJ8IHBH jClTHO a' 9J OaXOHSaBj * + 5 = 9 Blfff
Teopeuu SJIH HSKOTOPHX KJiaccos(3fr3 fleJiHTeJieft HJJIH. I.
20KA3ATEJIBCTBO. floeiaTOiHO aonasaTB, ?TO S/V -KOJiwiaBJieTBOpffiDT yCJIOBHK) eflHHCTBeHHOCTH HpaBtCC flOIIOJIHeHHJ! , T.K. KOJIBIJO,
aHTHH30MOp$H06 S/V -KOJIBIiy, CHOBa HBJIH6TCH S/V - KOJIBUOJ.
PaccuoTpuM paBencTBa (56). HoKasaieJiLCTBo c$opMyjinpOBaHHoroBCCTK c nowoiuBK) HHayKium no qjicjiy
/f =d(tfB)*cL(4B*). (58)
ECJIH /r=(9 HJIH /r=/ , TO yTBep^aerae oqeBHaHO. npeanojioKHM reneps, qio yiBepsaeHHe TeopeuH aoKasano JJIH scex /c<m-n nyciiHeKOTOpHX COOTHOJUeHHfl BHfla (58) K = m f m.>± .
B cajiy TeopeMH 3 qeiBepKH (fl,B,C,Z)) aBeTCTByraipe paseHCTBaM (56), Jinfio npHHaflJieaai HHOxeciBy A^ , JIH-fio nony^aMTCH MS ajieueHTOB sioro MHOseciBa c HOMOBIBK) onepaua^ I)-
PaccMOipHM
raec(.0eA7 , ot^+.£ nony^aeicH H3 oC^ c IIOMOIUBD HeKoiopofi one-paimH I) - 4). 0 TaKHx nocjieaoBaie^BHOCTHx (59) dyaeu rosopnTB ,ITO OHH oOpasyat aenoiny.
lenepB , ITO naine yTBepx^eHne aoKasano ^JIH scex(56), aJifl Koiopux K=rn H oana as
6CTB SaKJIKUHTeJIBHHft 3JieM6HT H6KOTOpO{t UCnOIKH BHfla (59) fl^HHH /T. .
ECJIH AZ=/ , H, HanpHuep, ^eTBepKa (fl.B.C^'D) Hiiee?TO
ECJIH xe TOTsepKa (tfj&^tyiateeT BHS (i,t,i,i) ,TO(fl,Bf,C,D*)ntw* BHS ^,5*/,Z?*;, i.e. B *=?)*.
IlyciB xenepB leisepKa (^iBfC,'D)QC'SJ> saKJiBiHTeJiBHHflneKOiopofl qeno^KH SJIHHH
PacciioTpHiiI) <*„.+! = pC&n). 3TO 3H8WT, ^TO 0̂ ^= (C.jft.fl, B) . Ho
yiBepsweHHe TeppeuH cnpaBeaJiHBO #JIH paseHCTB
Oic»aa cjieayei, vso yTBepaweiuie reopeira cnpaBeflJiHBO H RUB.HHX paBOHCTB.
48 JI.A.EoicyTB
2) y
ECJCH cL (X)=d-(y)=0 , TO flan flOKaaaiejiBCTBa Hyraoro Hau yr-HeOdXOflHMO IIpHMeHHTB HHflyKE[HK> HO flJIHHe aetlOIKH. ECJIH K6
HJIH d-Cf) OT^HMHO OT HyJIH, TO npHMeHHeTCH HHflyKIWfl HO
/r (CM. (!?8)).3) oCn.+ i — ctC^-n) • STO osHaiaei, ITO
npMMeHHTB Tenept HHflyKimio no
= ° C ' T0 eCT£
(d, B, C,2>)= (d.+C^
Biopoe as paseHCTB (56) npHnraiaeT
113 npea^oKeHHS HH^yKUHH,noJiy^aeM, ^TO cymecTByioT TaKHe sne-3 D E W. ?
Ho Torga
ECJIH npH aiou paseHCTBO (fl,B,CJ7))me6T BUZ? (9. id), TO BCTL
#=axw,TO MS (56) cjieayei,
paBencTBO flB=C'J) He raaeeT saaa (9.2). Toraa B caaynoJioaeHHoro BHine, nojiyqaeu, wo nepsoe as paseHCTB (56) yao-
ST ycjioBHHu (51) a Toraa , B cajiy jieuwH 3 , aonax7 ' D' S>'<T\' D *' TI*1TaKHe sjieueHTU H^,€^,0 , Z/ . wo
^'C.'2?'). (60)
reopeuH win HeKoiopnx KJiaccos(3ea aejiHTeaieJi HyjiH. I.
, 'W1). (si)K paseHCTBau
MOKHO npHMeHHTB nepBoe npesnoaoseHae HHflyKiiHii no A- . . noaioiiyB0 ,1)o ,E ,/-"
E
7)*= [
H ^erKo BURSTS,
TeopeuaCJIEflCTBHE I . S/V - K O J i s a a H B J I H B T C H GLB
20KA3ATEJILCTBO. IlycTB ft=P(S) - neKOiopoe, C - ajieueHTH as /2 Taraie,
flP.nCR.tO.810 BHaiHT, qio cyieciByor ajieMeHiu BfDeR. , yaoB^eTBopflioiniie co-OTHoraeHioo
(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
Ha npe;zwyiero BHSHO, ITO ct(_F) = 0 , TO ecTB /•*•-
9io
CIEflCTBHE 2 . C y n e c i B y i o T (? - K O J i t u a , H eB J I O K H U i i e B T O J i a .
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:
Teneps R, - KOJILUO co cjiaduu ajiropHTUOM (CM. [21 ).HoKaaeH, iro GCJIH
(66)
(^,8,C,D€P('S) y Ct(tf)>d(C), TO cymecTByioT TanaeR. ,
(67)
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
(67).
(67)
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.
top related