Osnovy teorii Galua.

~ 4. p-a~iu'tecmue PROWbl18 181 He H~pHmeT rPpH3OHTaJlbHrOI' nooJiKeH514. H~c~ombie 3Hat1eHI15 p 6yAyT paBHbl TaHreHcam yrJIOB, KoTophie OTpe3KH rIoJyqeHHOl JIomaHO~A o6pa3yIOT C OTpHuamnbuibIM Ha! paBJieHflem ocI Y. EtI~e Harngautee HpeJJCTa~HTC14 rlpoilecc, ecji Mbhi OKOJIO HaHBbICIweh TO4KH 3aKpeHHM Hillb H nycTHm ee BJROJlb OTpWiiuTCe~bHiOf OCH Y, a B HaHeceHHbIX To'iiaX Bo6beM rBo3Ju4IK1. 3aTeM 6yaem OTBOA1HTb CHo6OaHbfi~ KOHel4 HHTH4 BLnpaBO. HIpH 3TOM HHTb 6yjieT 3a1LerTnflrbCf 3a. B6HTbIeI rBO3IIHKHI H4 pHHmeT rioJIoweH14e J1omaHOR, jtaioigefl jWifl HCKOMble 3Haq - HHSI. He Baa3BaHCb B;ae~anR 3T0F0 fipoitecca, o6pa-mm JIHLWb BHHmaHHie Ha TO, '4 0 OH aaCT Ham POBio fl pa3JIo)xeHHtl. B camom jteie, OpJHHaTa HaI4Bb[Ci-neil 113 HaHeceHHb1X TOqeI( p"BHa CreneHIl fl Hamiero ypaBHeHU$1. IyCTI, nep~asi 143 cjieJiytoHIHX BeplIIHH JIOMaHOfl 6yaeT 'imeTb OpJ1J2HHTy fl2, H rIICTb CO0fBerCTByLO11u4A efl 'IJICH ypaBHeHHS (4.2) 6yaeT p'?C2x '. Tor~aa. onpexieuefflbsi K031)4wueHmra. a mbi nOJIyq4M ypaBHeHHe cz n +2 c. an 0, timieioig~ee n I-n2 OTnTH4Hb]X OT HyJ1S KOpHefl. To'IHO Tai{ we.iuii onpexie-.TieHHSI KO30pcJH1LtetiTa, a, COO T~eTcT~yOILueI'o pa3JIoxK~emo C HatlaJIbi~b1M qaieHOM opP, raLe p noiiyqaeTC5i 143 BTOPOrO OTpe3Ka JIomaHOPI, 6ya1eT CJ1Y>KHTb ylpa.BHeHHe -2 C2 =a' 0, mmeionmee n2-n3 OTJ1HqHbIX OT HyJIS KOpHetl. Paccywxaal TaHmm o6pa3O~i xa.'bwHe, Mbl HaKoiei JoIftLaem 110 ocH a6cuiLcc; B 9TOM Cniy'ae n. k 0. Bcero 6y11eT (ni - n2) — +(n2 -n3) + *..+ ('k-2 -nh-l) + n2k ~ pa3J1o)eHH4 4iA51. H T. 11,. 5. TH pa3JIO>KeHHH JaaIOT BO3MO)KHOCTb caeJnaTb HeKOTOpbIe 3aKJHoqeHH9I OTHOCI4TeJbHO rpynn~bi [Fanya ypaBHeHHS1 (4.2). HTo6bi 4)OpMyJ1HpOBaTb OTHocmI1LHcs1 ciojaa pe3yJlbTaTbI, BBe1LeM HOBoe [IOHRTHe [114 K JI a p) a 31 Row eH HA~. HlyCTb Mbl Hmeem pa3.TIo)KeHHe (4.6) a~p Xi + a2ps +., rae )1, x2,.. npextCTaBJneHbl, KaK Heco )paTHMble lpo6H4, H riyCm s eCTU o6tuHf 3HameH'aTeJ16 aTHx a.-o6efl (XOTq 9THIX 11po6efl 6eCq4Hc'ielH~oe mHo)KCCTBO, HO HX 0OU6Au 3HaMeHaTenTb, KaK MO)KHo 6bu10o 6bi rOKa3aTb, Bbl%IBngIeTCH Y)Ke Ha HeI(OTOPOM KOHexHHOM meCTe, Hnojio)eHi~e KOTOpoIrO 3aBHCHkT OT 11HCKpHiMHHaHTa, ypaBHeHHS1 (4.3). To'4Hee, cymleCTByeT TaKoe r, 3aBHCSIuLjee OT JLHCKPHMHHaHTa ypaBHe11HH (4.2), tITO eCJH 06a[1Hfl 3HaMeHaTeJm Jlpo6eft A', Ix2,.-7. Xe CTb 5, TO 3HaMeHaTeJnb KawK1oft nocJne11youLei 1po6H Xr+ m' m > 0 eCTb eJLIJHTeJ~b tuHcJiia s). HO)ICTaB.Trnsl B pa3hIO)KHHe (4.6) BmeCTO p, nocjCJIAOBaTeJbHO BeJiH'iHbi SP, e2p?,..e8 *p, rite 2zti =s e', mbi nojiytiHim ele S — 1 pa3JIO)KeHHfA, KOTOpbIe TO)Ke 6y11yT pa3 -)lo>KeHHSMH KOPHetA ypaBiH~HHI (4.2). 3mH s pa3Jlo~leHHh COCTaBBST UIH KJ pa3JIow1eHHfl s-ro nlopqa1Ka. FlpH 3TOM HimeeT meCTO

/ 232
Pages

Actions

file_download Download Options Download this page PDF - Pages 177-196 Image - Page 177 Plain Text - Page 177

About this Item

Title
Osnovy teorii Galua.
Author
Chebotarev, Nikolaĭ Grigorʹevich, 1894-1947.
Canvas
Page 177
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/acr5415.0001.001/185

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.