Osnovy teorii Galua.

.8-4 84 Ii~~~~~1. rpynna rajzya IIOJHHOM, He H3MCHINOLLUHA BeJIH4HHbl nliH Bcex HoJACTaHoBIC`X rpynnu~ rajiya ypaBHeH Hq (41) HnfCTb' a 6yateT 3Ta BeJU{4jHHa (qtHcjno, 61.rrb mo}KeT, HppaLlHoHajibi-oe). Pa~iieJ1Hm (1 (x1, x2..,x i)Ha f~ (x1,2,..,x~1 OCTaTOK He 6yJ~eT 3aBHceTb OT ~,,, TaK KaK 1.141 MOJLyJRb nepB~fi CTeneHH H Hl npl =X, )XQJ1H nHlHH1ImaTb 3Ha'IeHHe a. 3Ha'rnT, Oli BOo6nte papell a, B nIoJ1yqHHOM BblpaweiiHHH OCTaTKa 4D (x1, x,.,? 3aMeHHM X Ha H pa3,aenlHM Ha (nl-)-Ht OCHOBHOfi MOaJlYJbJf xX,.. 2 OCTaTOK OT ateniie~ui (D.2 (XIx7.,x, f H1HHHMaeT HplH xn 3HaqeHHe a, T. e. ypaBHeHHe (4.13) (1~42 (XI' X2,..,Xn-2, 1 ) a, 0 HmeeT KOpIHem x= x-1. HO TaK KaKT BeJIHqtHH (1) He meiisi' 3HaqeHwSI nPH HO.ICTaHOBKax rpyntiii F'anrya, a rpyrinia F'ajya couiep~xwr notCTaHoBK0, 0CTaBBJ11IOu1He X1, x2,..,X"- Ha meCTPC H- nepeBOAR~ivue X,__1 B.nio6otl xO peHb (n-l1)-ro ocHioBHoro MOaiyJU, TO ypaBHeHiHe (4.13)1, 6yatyql CTene1fHH HHfDK n n-iV Hme II_ Kopiiefl H n1OTOMY 51~si~ie-rCq TOwKJeCTBOM OTHOCHI TenbHO ~ 1- 37170 0311a'iaeT, 'ITO q'2 He 3aBlCI4T OT 1-I(1)'2 (X1, X2,. -.,: "-) - =a. BO Bpem4i 1IOH3BOJLCTBa oriepatitifl iawii 4~YHKLIHH, nepeC~a~aal 3aBHiceTb OT HelKOTO~b1X KOpHei4, B TO we Bpemg HaqiHHa1OT 3aBucem- OT 1<034411 -Pamxe-nM (D (XI, X2,... X~- tt-2) Ha (n-2)-ft MOJayJb. - OCTaTOK OT a, T. e. ypaBl-e~we (4.14) 1 (,x2.., 3, 2)-a - 0 1mmeeT KopeHb ~-n-2 =x%-2. Ho 471yHKLLH11 (D. He meH1eT CBoefl BeAW-urHNb, QCJ1H, OCTaBJ151B ua meCTe XI, X29.. Xn13, rnepeaeCTHi X n2 H rno6ofl zApyroft icopeHb (n-2)-ro OCHOBHor'o MOJayJ.f. HO03TOM y paBHeHHe (4.14), 6yayy'm CTenHlHH HH)Ke n,-2, B TO ~Ke Bpem~i HMmeT nfl-2 KOPHR, 'B CHJIY liero OHO.aoMKHO o6pamambCg B TO>KAJneCTBO, H T. Ji. Hlpo,?ioaimaa 9TOT npoluecc, m,0 B KOH1Le KOHtLOB oCB6oJIHm Bb1ipaI(eHHe Hawletl 4)YHKLUHH OT Bcex KOPHCA1 X1, X2,.., X,,,H e BBOJUI HI4icaKiix Hppauioia4OnJbHUdX BblpaNi~eHHII (Beawtrna 0 He y4aCTByeT B npoiueccax JeWeJiCHH). HO3TO~ly Mbl HjOJl'qHM uIIIwuf 4)YHKBMHl (. e. XWIHl BenJ1H4H~bI 0) p —ltLlOHaJ~bH~e iWipaweleife 'Iepe3 K<031411H1iHCHTbl ypaBHeHHS1 (4.1), '-I. H1 T. a.1 ECIHS FD(x, X2,,..,x,) XJ pO6Ha'i pautmoa.TbHasi 4)yHKILH5, TO Ham uipl-.laeTCf1 fOBTOplHTb qacmb 20 Al2Ka3aTe.1bCTBa Teopemb1 41. 12. HaCTrolultee H3J1o)iKeHHe OCHOBI TeopiHH Iaiya OTAIH taeTC1 'OT ot5itCeIlpRIIIToro KfiaccH'qeCKoro H3JIO)KeHH51. Halel! -Toro H3JilOwCCi'1H, HpHHaviUemKuwaA MepTeHCY (P. Mertens), pa3BRTa 6oiiee 'n o)a p o 6LTO B JLHccepTalUM C. 0. UiaTyHOBCKOFO..TleBlI (A. Loewy) He3aBHCH'M0 OT LI~aTyHOBCKoro pasiBen.f TeOPHlo, BPCCbma CXOaLHYLO C TeopmeiI WLai~yHOBCKoFro H JiaYRLY1O HecCOJnbKo aamee. rio H310oeHIIC timeeT, C OJLHOiI CTOPOHbl, TO HlpeHMYHLCCTBO, 'TO Cpa3y nIOuJXOJLHT K CYTH xAena, He npH6eraq K HCKYCCTBeHHblm n1OCTPOeHH5I1M. C arpy..

/ 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/acr5415.0001.001/88

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.