Osnovy teorii Galua.
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~ 2. Hen pU6.!9ul~be llOAU1iOibl 65 Torjjaa ii~ ~ ~ ~ ~~~i D (F) = (F, F') = ~ [f (xi) g(x,)' Fl [f (y1)g(y1)1' = 1 H [(xi)g'(xi) 4-f'(X1)g(xM) H If 0ylg'(y,) +f'(Y,)g(yi)] OTKyJaa B CIiMY f (Xi)O 0 ii i)~0.(1.13) D(F) =~ Hg(x1)._HJf(xi) -_Hf(yi)._fl g'(yi)= =~R(f.f'). R(gjg') R(fjg) R(gjf), JIMH (1.14) D (f -g)= D (f )D (g)J?2(fl g). B 3TOfI cjpopmyJe Kawa~bifl [13 JLHcKpMiniwiaITOB H pe3yJlbTaHTOB npaB3oA MaCTH eCTb Laeiaaf pa[u4OHaJbHwi 4)YHKR1J51 C. u~ejuimli K034)KPH[LieHTami4 OTr K~o94qHIu~eHT0B HOJIHOMOB f(X) H g(x). H/3 Hee cJneayeT, 'ITO KawfIbflk [13 MHO)KH~eJnef npaBOfl MaCTH eCTb aTeJIHTCeb MiHcIa D Uf. g)... Popmyna (1. 14) aoriyCiaeTr HPOCToe o6ofuierne Ha c.jiy,4aft npOH3BeJLiHHlff MHOi'X F1OJIHHOMOB. HmeHHO, noniaraq F(x) = f1(x)f2(x)..., fj~x), mbi rIOJly'IHM: k (1.15) D(f1.f2.fk) ~ HD(fj).HR2(ff) ~ 2. H1pHBOAnmbie H He1piiBOA~HMbIe IIOJIHHOMbl. 1. nHo.wre HeInpHBOAHtJMOCTH. B TeopHH raiya.9BJII1eTC51 OCH0BHb1M I1OH51THe rHplBO01RHMOCTH14 HeripHBOILH4MOCTH IojiLHHOMOB, TaK WIO Ham Heo6XOJ1HMO Hay4HTbC%1 npHnHOMO[LLH KoHeqHoro liHnla JaeFlCTBHfl pa3 -JIH'IaTb, R1BA~f1TC51 All Ka)KJUbIfl 3aJaaHHbifl nIOJ1HHOM 11PHBOA1Mb1M 14,11 BeT. PaCCMOTpHM C~tin HOJIHiHOMbl C patuiHaHJ~bHb1MH K0344n[lMHeHTamH. Hlo.IHHOM Hu3bIBaeTCf1 nIp H B0 RH M blm, ecJii ei-o MO)KHo HpeJLCTaBHTb, KaK flp0H3BeJaeH~e IIoJIHHOMOB C. pa~uHoHa~nbHbM1Mn K03(44HpiuteHTamH4, KaxKJabfi~ [13 K0TOpbIX 6wi 6Mi 6oniee HH3K<0fl Creneffl. EcJIH Ke 9TO HeBO3MO)KHO, To nloAWHI-1M Haub1BeTCR1 HenpHBOJIHM~blM. 2. ]J~Jr HaxOueKJlfHH1 UiplemOB, nO3BOJIHIOLILX npH nomoHJ" KOHCL1HOP '1HcJI AeA1CTBHiM pa3JIH'laTb HpHBoJJJ1mb1e H 11jcrIpHBOJU4mbie HOIHHOMbI, BbIrO,1HO nepeAT1T K n1oJ1Hffomam C 1LeJbIMHi Koa43HLUieH~aMH. Toro MOWKHO jierFo 'OCTHrHyTb HlyTem YMHo)KeHHI rTIOIH~oMOB Ha o6umil 3HMamHaTuIb Bcex KO34X(3HuiieHTOB. Kpome ToIro, yao6Hee HimeTb aeJIo C HoiJIHomamH, y KCOTO~bIX K03(~4Hl14HeHT npH CTa1pL1eM TuieHe pa~eH eAtHHHLue. HlTO6bI repetiTH OT [IPOH43BOJIbHoro ugjioqtcnceHH~or nOJIHHoma K L1jeJIOl4HcJ1HHomy nol0H-OMY CO %-TapUlHiM K0-4cJ)(iHLHeHTOm eJLHHHLua, caeie'aem B Hem n10JCTa1HOBKY y= -a- a 3a~em YMHO>KHM 3TOT [IOJIHHOM Ha A. n-il Hlony= nII, 4HITCR nOJ1HHOM Tnna (2.1) ao ~alx + *. +a x1 + x'. 5!e6oTa-pen,.
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About this Item
- Title
- Osnovy teorii Galua.
- Author
- Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
- Canvas
- Page 57
- Publication
- Leningrad,: Gos. tekhniko-teoreticheskoe izd-vo,
- 1934-
- Subject terms
- Galois theory
Technical Details
- Link to this Item
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https://name.umdl.umich.edu/acr5415.0001.001
- Link to this scan
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https://quod.lib.umich.edu/u/umhistmath/acr5415.0001.001/69
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DPLA Rights Statement: No Copyright - United States
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https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acr5415.0001.001
Cite this Item
- Full citation
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"Osnovy teorii Galua." In the digital collection University of Michigan Historical Math Collection. https://name.umdl.umich.edu/acr5415.0001.001. University of Michigan Library Digital Collections. Accessed April 30, 2025.