Osnovy teorii Galua.

IlcmopuwlecKuul otteppK 11 iae, p, p'P",...- ripocmie 414C/a BHJaa I ~ 2'1. OAF19Fco TOJUbKo 6.narolrap.5 Teoput1 ranya, IofBHJnacb yBepeHHOCTb B HeBO3MO>KHOCTH 3aamai n si aTIIxpyri~x cJayqaeB. 7. Teopjii~ ranya H aJare6paHqecKHe [JHcjia. Oco6eHmo r~ny6oKtie nptiJIoweHIH9 Teo.1pHH [ranya aLofnycKaeT Teopiisi ti~ceJI. Bornpoc o6 apHi~m~eml~eCKOfl npnpo~le KOpHeR ypaBHeHHH, KaK B6151CHH4J1OCb, TeCHO CB513aH CO CTpyKTypork ero rpytnnbi rajiya. BOT nepBbEfl pe3yJUbTaT B 3TOM HarnpaBJIeHHH: KopHH4 BC5HKoro ypaBF~eu~lf c a6enle[ofl rpynnott raiiya B IoJIe pa1LHOHaJ~bHblX qiicen, Kaic o6naacT pa~lUoHaJlbHoCTH, paLJJHOHaJnbl-1 Bblpa}KatoTCH qepe3 HeKOTOpbie KOPHH 143 eJLHHHLUb, *oTropbIl 6buIi npe~iyraiaaHi KponeKepom (L. Kronecker) H BflepBble C~poro Jt0KB3H Be6epoM (H. Weber). B HaCTo~itee Bpem5i cy1LueCTByeT OK0O-1 awC1TlH pa33JH4HbTX xto1a3aTe)IbCTB 5TOfl Teopembi. 1(POHeicep 3aaaciaJC )aaablieflURHM Bonpocom o6 yparnieuiwix c a6enIeBoft rpynnoft B o6aaTlac paimlJoaJnbHoCI'H, o6pa3oBaHiofl MHHMfIMH KOPI14M14 KBaaiL paTHOEO0 ypaBHeHHHf. OxuanaoCb '(ITO TaI~oro poiarBn HCJ1iHbi no.iylaloTC5H, KaK 3a',iaCHHq 3JIJIHFITHIeCCFCHX 4lYHK[LIA, JLoIyctKaio1LLX Tal< Ha3blBaeMOe KomnKOJc FCHo yMHO>kKeH ie. Kpo~lCKep npeJLono)KHJI, tITO 9TH 3HaqeHH% RaIJYT KOPHU BceX B03MO)KHbix aGCJICBbIx ypaBHeHHMi B paccmaTpHBaemof!,o6AaCTH pat4liOHia~bHOCTH (,,Jugendtraum "-me'ITa DoHOCT14). 3T0 fnpeiiioR0 -weCHHa ytaanocb B o6amem IoLB3aTb cPy9Tepy (R. Fueter), HplH4em o1~a3aIc% OJLIIH HCKJI ~tHTe~nbHblA cy~iyag, He BKJ11qaoLU1HIHAC5 B 3TH 3HaqeH14ll. Hccnieyap apHC~meTWICK14e 3aKoHbI i(omI7IJLKCH~frO YMHO)KeHHH, 4'y3Tep npHiwe~a K o6mum 3aKoHam, Hmei=flHm meCTO X1U2 ypa1UHeluifl, a6e~ne~blX B npOH3BOJ~bH-OI o6JlacTu paLIoHaJ~bHocTH. 3rk1 3KOHbl1`103BOMfflIT paccmaTplHBaTb none KOPueP-A TafCIIX ypaBHeHHf4, KaK o6o6umeH-le TaK( Ha3. Kiassenk~rper, H CHB53SIBaIOT c-TCHreCfb.9T11X ypaBHeHHI4 C 'I H Ci I 0i M H J e a Jibb H bl X IC JI a C C 0 B B paccmaTpHf~a —mof O'5JlaCTH pauJ~ofia.TbHOCTH. 3eCcb BCI(pb1HaeTCHl rliy6oKaq C3143b mCWAt TeopHefl Jranya H4 TeopHiel 14ar e a ni B, I(OTOpbLe SIBJIIIIOTC9 OCHOD3b1M HHCTpymeHTOM B TCOPHIM aJlre6paH'IeCK14X 'iHceJI. TaKarvi (T. Takagi) jaan 3aKoHqCHH~blt BbIBOXL yIiOMSI11YTb1X 3aKOHOB. 8. CBS131 ypaBueHHii co cpaBtieHH4$IMH. 13 TeCH~fI CHB53H C YH0MSIHYTbIM1H.3aKOHamH4 CTOH4T 3a1{[OTI, 0OTKpbITb11ri Ue,JI-LK4HHJoM (R. Dedekind), (Ppo6eHI4ycom (G. Frobenilus) H rypnB'u~em1 (A. Hurwitz) H B Cnoeft 9JICMIM~pHOJI qaBCTTI moryLLLHm 6bITb 4~OpMyR14pOBalH Taif: JIUaH HO1JIHHM f(X). PaccmaTp~fBa14 ero in MOXaYJ1IO HeKOT0POFO npOCTOFO tuiucia p (T. e. i4Me51 npai~o npI16aB.-,1,Tb ic ero 1Cc3(~~4I1umeHTam K~paTHOCTH p), pa33Jo)Hm CeO Ha HeHpHBO)1i4Mbie AMHOIKHTenti. rHYCTb (3) f (x)xA-fl(x) fz (x)... f,jx) (m od p),I rje fA (x), 12 (x)..,fk (x) Her1pHiBOiLmb1e no MOALYJ1O P nOJIHHOMNI CTCel-lef nl, nl2,*~ nk. Touraa rpynna Faunya ypaBHeHHS1 f (X) = 0 coJLep)fHT nO)1CTaHoBKy, coc~ro~inwo 143 UH4KJ1OB HOP5AKOB nl 'n2, ***. nk O6paTno, ecCJH rpynria Faiya, ypaBHeHHH1 1(X) =0 coaep)KHT IoAMr110BKY, C,)CTO$IWIYIO 13 LLHI(JoB nOp14aKOB 11, ftl, TO CyH4eCTByeT 6ec'qiHcjieHHoe MHoflceCTBO TaBKHx n1pCTblX qiHcej1, JTIFI KOTO~blX HmeeT meCTO pa~iio)Keii~e (3) QOpo~eHIRyc). Kpomze CBOHX rnpHJ1o)KeHHft B T opHH4 aJnre6paH'IeCKIHx 'Hceni, 9am Teopema 1IO3BOJIf~eT YCTaHaBJIH~aTb, o6injie KP1ITepHH JRl1 HaxowaeLHH5I rpynnbi OTJAlbJI111AX KJiaccOI ypaBHeHtf14, a TaI0K YCTaHaBJIHBaTE ToxKJLCTBO JiBYX 3aXUiHibix

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages #1-20 Image - Page #1 Plain Text - Page #1

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page viewer.nopagenum - Front Matter
Publication
Leningrad,: Gos. tekhniko-teoreticheskoe izd-vo,
1934-
Subject terms
Galois theory

Technical Details

Link to this Item
https://name.umdl.umich.edu/acr5415.0001.001
Link to this scan
https://quod.lib.umich.edu/u/umhistmath/acr5415.0001.001/15

Rights and Permissions

The University of Michigan Library provides access to these materials for educational and research purposes. These materials are in the public domain in the United States. If you have questions about the collection, please contact Historical Mathematics Digital Collection Help at [email protected]. If you have concerns about the inclusion of an item in this collection, please contact Library Information Technology at [email protected].

DPLA Rights Statement: No Copyright - United States

Manifest
https://quod.lib.umich.edu/cgi/t/text/api/manifest/umhistmath:acr5415.0001.001

Cite this Item

Full citation
"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.
Do you have questions about this content? Need to report a problem? Please contact us.