Osnovy teorii Galua.

136 136 ~~~~IV. r7puAOJCeHUR meopuiu I'aiya TenepEb AoKawem, Wio HOAiHHOMbI fi(x, y) HenHlHBOJUHM1 K o6Aacmp K(y,). [IYCTEb, Hanpilmep, X -X1 9BBAHTCH KOPHeM HenlpHBOJRHhiOjO B o6yiaCTH K(y) IIOJHHoma I(x, y) C~eneHH~ 1 -<MpHa KCOTOPUR~ aIeJIHTCH nOJIHHOM f4(x, y,). Tor~ia Z~ = Cp (Xi, yj Siasimerc KOPHem nojiHHOma h, (z, y) CTe-~ rneHH vc Ko94XI3HLLieHTaMH 143 o6naCTH K(y~). V-IOJ1HHOM h4(z, yl). h2(z, y2)..h/(x, yj) I CTen~eHH nlv, HmeeT K0,34XPIll~leHTI 143 nepBOHatianTbHoi o6JaaCTH- paujHoHaJab-~ HOCTH, a I1OTOMY JAonweKH aleJHTbCfI Ha HenpliHBOJMbit nOJIHHom Ii,(Z) CTenleHH ftkfZ, 14nmpHeio1IHR KOPHem Zj. FLOSTOMY iimeeT meCTO TaKH{e n v, >- nm,,, '-TO B CB513H C V < Mj 2tOMIKH(O JLaBaTb IV =m,, a STO yKa3b1BaeT Ha TO, 'iTG nOJIHHOM f,(x, y~) cowaraute c HenlpHBOAlH~bim noJiHHOMOm fi(x, Y~)* OTctoua cne~iyeT, '-ITO B no~ie K(y) HOJIHHOM 1(X) paaiuarae'rC5i Ha He I1pHBOJA4mbie HOJHHOMbl cJ1neapou1LMm o6pa3oM: B camom.IeJle., KaaKItd K~opeHb IIOJIH4HOma f(X), H-arlpHmep xi, jiaeT KOpeHb <P(X,, Y) f0lWHHOma h(z), KCOTOpURi aioJDKeH 6blm KOPHem KauomHH6yJ~b 13 nloJHHOMOB hi(z), HanHHmep hj(z). B STOM caiytiae XI B cHJ1y (1.4) AIOJJ)KeH 6bzmb KOPHem nHOJHoma f1(x, y). C JJpyroft CTOPOHbi, noJIHombI f1(x, y) (i = 1I 2,..., e) He mor~yT timmT o6uwix KOpi-e~t, TaK Ka3K Tom~a 6m~ H n1OJIIHOMbi h,(z) (i = 1., 2,f..., e) HimeJH4 o6jige KOPHH, a STo npOTHBope'-HT onpeitezieHIO HX KopHefl p (x,, y) AHaJIorH'iHO Hmeem cneapyoumee paaiioweH~e UIOJIIHom a g(y) Ha tienplpHB JAHmbl ii o6JnaCT1 K(X L) no-qrHHoMbJ: fHpHHHma~l BO BHIMHmmi paBeHCTB-O (1.6), nowy'aem T e op emy 73. fHyCmbfiX), g(X) HenpiiBOJLHMbie nOAHHOMbI, XI, ~YlKaKtie-HH16y.Ltb HX KOPHit. EcJIH f(x) pa3ilaraeTC51 B o 6.aaCT K(yl) Ha e HenpHBOJLHMbjx IIoJHHOMOB, TO g(y) pa3.narae'rc B o6JiacTH K(x1.) ToH{eHa e HenpHBO.LHMb1X HOJIHHOMOB, riHqe44m TH n1OJ1HHOMbl MOrYT iM, 3aHyMepoBaHbJ TaK, 4lTO6bi CTefieHH HOnII4HOMOB B o6oHx pa3Jo}KeHHHX 6wAH nponop~uHOHaJEbHbi. Teopema 72 RBfifeTCfH,aCTHbIM cjiy'iaem WWIf Teopembi. 4. Hecm~oTp5i Ha TO, '-TO fl1fHBCeaeHHoe HaMH JAOKa3aTenbFCTBO Teop~emb 73 coeepmueRHO 3JnemeH~apH-o, mbi fpHmBe~tm ewue nepBoHa'4aJabHOe JlOKa3a-reJbCTBO ATaHac6epra (G. Landsberg).3TOfl Teopemui, TaK KaK OHO COrlpOBO)KAaeTCST Ae~TaJbHbim aiiaJIHOM BXOIRUIHIHX B paccy)I(LeHHsi rpynn mi AaeTr 6onee nonlHoe npe4tcTaBJaeHHe 0 rpynironog CTPYKType nonTy'iaembix pa3JIO>KeHHfl. PaCCMOTpHM HopMaJ~bHoe nonre K, o6pa3oaaHHoe KOPHRMH o6otix rIOJHHOMOB (1.2) H (1.3). HyCTb ero rpynna 6yleT (% 14 nyCTb KopeHhx X1ypaBHeHH5J (1.2) npH~anaie)Kvr K nouirpyrine Wi, a KOpeHby, ypaBHeHH51(,3 K no~rpynne 032' Pa3JoiinM 63 no: 0.8) (1.8) i~k9 k+ WiS2 + - -+ WlSm

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 117-136 Image - Page 117 Plain Text - Page 117

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 117
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/acr5415.0001.001/140

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 May 1, 2025.
Do you have questions about this content? Need to report a problem? Please contact us.