Osnovy teorii Galua.

~4. rpynnarFaiya 8 85 v'Oa:V CTOPOHbi., ero 3Ha4eHHe 3aKJ1O4BTCH B TOM, 4 TO OHO iaaeT BO3MO)KHOCTb fHOCTPOHTb TeOpI4io raaya, He fIOJb3ygICb Teopemofi 0 c34LuCTBOBaHH4H KOpHeft AARn~.9Toro cuieaiyeT pacapl~~ COOTHomLeHlig me)KJa KOPHMHMI He KaK paneHCTna, a KaK c pa BH eHi H i. B camom JteJe, paBeHCTBO (4.10) nIOKa3bIBa~~T, '-TO iie~a% qaCTb, BCIKoro coOTHOIIeHH9 meWKXY KOPHR1MH RBJIfIeTCH OJ1 -HOpO~LHOPl JIHHeflfHO11 KOM6Hffauji4ePI OT OCHOBHbIX- moatynref. ECAH 3a1iHCaTf, 3T0 pa1eiHCTB3O B BI-IJe cpaB~eHH51h TO oupC~eeJIeHHbffl Tc-IKI4M o6pa3oM CHMBOR1 Cpa-.IBHeHii H 6y'aeT YJ1OBJIeTBOP,5TL sceM Tpe6OBaHSIRM, KOTOpb1e npeA-UMIBJlISIOTC54 K 3i-y ~pa BeHiCTBa. H03TOMy BCA TeopHR [ranya moweT 6bITb H3JO}KeHa H HpeJariowOeHi4iii, 'ITO BeJIH'-I4Hbl X, X1..., x4, npoCTO [iepemeHHble, HO 3aTO B p0O11H paBelCTB3 paCC~laTpHsaTh TO.JbKO '-IO YlOM54HYTie cpaBHeHmi4 110 4)YHKUlioHa)1b-IbIbM MO11IYJ5IMN A7 fe,..., f,, B JtHcepTauiH4 H~aTyHOHcKoIrO TeopiuiI'aniya npooeae~a H4meHHO TaK. KOHe'IHO, HPH CTporom- nIOBeJLeHH1 SToro n1pHHI1HH Bce JtoKa3aTeJlbCTBa HIPOBOJARTCR CJIO)KHe e, rnlaB[FIbIM o6pa3om 6uiaro',ap~i YC.UO1KHBI3ILL1MC51 *603Ha'IeHRnm. 13. fH p Hi m e p. PaCCMOTpkHM ypaB~ieu~e (4.15) ~~~f x)= X P1}x '-2~...4 x+ I = 0. 13 ~ 2.9 Ml. BHli ie JI, q- TO 3TO ypaoiieiive HeInpHBOAHIMO. C JapyrorH CTOPOHbI, 0O0O 2 -ri wHa'Iai l~epe3 x1 ero icopeHb e ' MbN Bbipa3HM liepe3 Hero OCTanlbHJAe KOPHki TaK: (4.16) x2=x,',~~~ XI~x,., x,, — x Ero riepnW!! OCHOBHUQA MOJAY.tb e2Cm f (~,), B TO Bpe2mii IaK Bce MO)yIYIi, Haviimia CO BTOporo, fIBJIIOTCH jiHH1ierHhiMH [IoJIHHomaMH. AeH12iCTBHTeJU HO, B rIwAe k (x1) nomjHOM f(I9) pa3i'iaraeTCH B cuiiy (4.16) nia ciielyioutte atitiehl~ble MHo}KIITenji: Ho03TOMy OCHO3IBHUMM mo0jtifmH ypaBHe2HHf1 (4.15) HBA5HIOTCq caeaJyIOLLLHe FIOAHHOMbI..4.17) P " P- J'+A~3 4Il TaKHM o6pa3oM rpynnia Fauya ypaBHeHH51 (4.15) HmeeT flOPIIJOK p - 1 3a F~pynala LLHKJIHqeCKaql. JAeH-CTBHTeabHo, o0o3HnaaR t~epe3 g nepBoo6pa3HblA i~opeHm4.paBHeHH5I 14 o6o3aqaHil qepe3 T IIORCTaHoBKY, nepe~oxiytuyo x, B x1f XlqB,..., 6paTHM BBHMHmaH1 Ha TO, 'ITo Tk 1iepe'5oAjw X1. B XY' (k = 1, 2,., p - 1). HO, TaK KICu P- 1 eCmb Hauimerbauaff c~ehCHb g, CpaBHHma3i C eJLH1muerl 110 MO1ylJO p, TO OTC10 -Aa 3aKIiiouIem, 'ITO T2' e CTb HaHmeHbu~as CreneC~b IIOACTaHOBKH4 T, paBnaff eAuN14 -ue. Ho03TOMy Bce HO0,CTIHOBKHI 1, T, T2,.., ' - pa~3JII'I-I~b H TaKI4M o6pa3oU MicwepnWbBaloT BCIO rpyurny [FanTya, nop9,lmOK KOTOpO1A paBeH TOwe1 p - 1. 14. HopMaambHble ypaBHeHnisi. ECrn BCC KOPHH4 KaKoro-Hi46yJ~b -ypaBHeHH49 AtoryTr 6blim pa~l4oHa.~IbHi BupaweKHbl qepe3 OAHH 1-13 3TH4X KOpHelfl, TO ypB IleHHe HubamffaTC H 0, p M a ui b H bi M. He TPY21HO y6eJHTTbC14, 'ITO ypa13H12HHe tiopmaJnbHO Toriia H TOJW.XO TOUaa, ecJiH Bce ero OCHOBHbie2 moJ.yJi, Hiia1U1ial CO BToporo, JIHHellHbl.

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 77-96 Image - Page 77 Plain Text - Page 77

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 77
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/acr5415.0001.001/89

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.