Osnovy teorii Galua.

152 IV. Tnpuzoxcenusc meopuu ralya ypaBHeHHtI, KOTG~bIM yJLOBJ1eTBOP511OT BeJIH'IIHWb COS 14 Sidl -f-. Ypa13He-. p p HHe YIHPOCTHTCfl, ecail Mbl BBeae~M B paCCMOTpeHHe BeJ1144HHbJ iT~~~~~~~~~~~~~~~~~~~ cos + isinp- e ZCO z+cs i - si~n ~.e p p (3.15) - et~ 0. BKAno0flM B o6.!iacTb paIlIloHa~qbHoCTH, Kpome el? eu~e P4A KopHb 113 2 -xi eeH~l =. — Tomx~ ypaB~eH~e (3.15 HiopMaJlbHO; B CaMOM JAeae, iff BBOJXJM o6o3HaqeHHe Z = e,MWi cmoKM BblP23HTb Bce KOPHH ypaBHeHH51 (3.1 5) TaK: OTc~oxta MO)KHO Ta1K}e 3aKwliIl4b, LITO BeaI4qHHa PS fBJI5IeTCH9 HaTypaIJlbH~tl lippaLUHOHaabH-OCTbIo. B CHJ1Y HopmaJnbHOCTH4 ypaB~eHHR (3.15,) Kawgaag nOXLCTaHOBKa ero, rpyntibi ['ajya mo)KeT 6WlTb O2IHO3H4atHO onpeaienveyia, ecrnH mb! 6yaem.3HaTh, B KaKof 143 KopHeft OHa rnepeBOJAHT iianpumep KO~eHb Z. HO03TOMy STH noX-~ CTaHOBKH4 moryT 6WlTb UpeJLCTaBJIeHbi TaK: BmeCre C Tem ypaBHel-11e (3.15) Be MO)KeT 1mmeTb KpaTHb1X KOpHefl, Talc xKal npOH3BWLHsf ero JleBofl 'ICT14 paB~a z- = pe: 0. lMccnre~ayeM, B KaKHx cnly'!aHx rpynna ranya ypaBneHINi (3.15) coalepHCHT nloJLciTHOBKY (Z -eZZ). HyCTb 1(Z, e Z, e 2Z, pp- x, e)= 6y~eT KaKoe-HH6yalb COOTHowIeHI~e me)Kly HOPH5MH ypaBHeHH51 (3.15). 3TO, COOTHOweIHHe MOWIHO neperniCam TaK: (3.18 ) XP(z, e>=-O. Ecrn* Be cy1laeCTByeT HHKaKoro ajnre6pawiecKoro COOTHOwneHII 13HAa X (eZ)= 0, TO COOTHOI11HHe (3.18), Han~calloe B 4bOpMe W(e P',e 0, 6y.1eT HMeTb. meCTo 11H BceX 3Ha'1SHHHX (p. JiOBTOmy, nOACTaBJIIIH BmeCTO ( BeJIH'IHHY cp + -,MW IoJyi~41m 143 (3.18): p W(az, e) = 0, OTmyza 6yz~eT cJIe1OBarTb, 'TO flOJLCTaHOBKa (Z — ~ Fez) BXOILMT B rpynnriy[anya ypaB~enxa1 (3.15). B 19TOM cany'ae rpynna yp&BHEHHHf (3.15) HmmeT n1OpqaJOK,

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About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 137
Publication
Leningrad,: Gos. tekhniko-teoreticheskoe izd-vo,
1934-
Subject terms
Galois theory

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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.
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