Osnovy teorii Galua.

18-q V._Ypoeneniui C 3UXIatnbLMU epyflvimu___

Hccnie~ayem rpynny 17ajnya OJ1HOrO 143 MHO)KHTeJnef BITOrO ypaBHern-n, Haripumep
(6.5) xV-i M x2 X ) O
B o6Jna,.TH pa1Ij4HoBJbH0CTH K( M~i)
3. fHpehiBapHTeJ~bHo HccJIf_!lyeM, Ha KBI(YIO CTenelib flpOCTOrO ml~cnia p aie-.TIFTCR 6HHOMija.ThHblf K034)4)HIu~eHT C],,, ecnH in 11 eJLIJHTICH TO4qHO Ha k-yio
CTe1JeHb p, S - H-a 1-yio CTeI1eHb p ti e ciiii _~P. Hmeem:
(6.6) C =M - -_ _ _ _ _ _ __3,aeCb B H4HCJIffTene 14 3-ameHlTe~ne fiounHPcaHbi Japyr HOJ JIpyrom MiWHOI4 -TeJ1H (3a i-icKiunlOeHflem mHO}KHreJm5 In B 'IMCJI1TeJe 14 S B 3HiamejaTeJne),.nenmri~uieCI Ha oaHy 14 Ty )Ke CTeneHb p. B camQm ejjeie, B CH4TIY i < S _P
4H1CJO i J4eJIHTCH Ha 6o~nee H3IM I0 CTe11eHb Hl~M n: C c. pi, (c.9 p)=1
t <k. H0BTOMy Li4cjio m-i )WJI14TCf T0)1~e TO'4HO Hia pt, H TaKHim o6pa30m C.,
ejJiM11TC14 Ha TV we~ CleeHefb J), 'TO Hi tiaCTHoe - 'loceJI, CTO$I-W4HX B '1HCJIH4 -Tene 14 3HameHaTeJae Bblpa>KeHH45I (6.6) 6e3 napui. TaKHM o6pa3oM Cm8,aJIH11TC14
TO4IHO Ha pk4. HlyC~ p - OhLIIH 143 MHO>KHTejiei4 'IHcJ, Fin, H flyCTb M = p MIn)
rie ml B3aHMHIO-HpOCToe c PI t114C.To. Paauo~iM KOPHH4 ypaB1IHIN5 (6.5) no
CTenHH5M P. HOIOI)KM x - s + ap. rae e 14 a - B3aHMHO-npocTbie c p
'I"cia, 14 nOACTaBHM B ypBe~ (6.5). Hlpui 3TGM 6y1LeM BbI[II4CbIBaTb
TO.TIbKO,,Onopnble" 4J1eHbl pa3JIO)KeHigI, T. e. TaK~e, y K0T0pb1X HOPSMKFOBbIe
'IHcJaa HPI4 HeKQTOpb1X 3HaqeHH51XP p>, 0 M0rYT 6bl~m MeHbwle, qem nopfIlaKoBhie qHHcJa apyr14x qIJeHOB.,,He-oaoplbiee" qnIHbI He 0IOKaWT HH4KaKro
BJAkIIHWI Ha IIOCTpoetHHe MHooro~PJibHHKa HbfoToHa. PaccmaTpHBasH pa3Jio}KemieC qie~a (s+ ap P)m, Mbl YBWLL1HM, H4TO B ero uineiiax C., 8&ens aspps nH~
IIOCTene~HHOM yBeJIm44eHHH1 s ero HO~HJ1I(OBoe 'IMCJO M02KT pa~CT1 6uarouRapq
M.HO)KHTeJIIo pP& ti y6blBaTb 6ularouaapH MHOfCi4TCJIio C,,,' HppH 310~ MnrpH
1 I s < p C.' eJIlJ1TC11 B CIJ1y 11. 3 iia Oa~ H Ty x~e CTeHeHb P (Ha k-io),
a pPS - Bce H-a 6oumrnlyto C pocTOM S. rlo3ToMy 143 BIIX 'IJIeHOB,,onopHbIM" 6yaue TOJ~bKO quieH- c -s =1. TO4HO TaK( we 143 'IJaeHOB C S <Sp2
MHOWK1ffeJb C,,,' aej114TCR110H KpaAiHeA mepe Ha p, 11 n1liTOM C],P'.ileJiTC~1
T014HO Ha p, a COOTBeTCTByIOmiiLI emy MHO)I1HTeJRb PppP- Ha camyto
HH3143I1O CTeneHb p,) B cH.-iy liero 143 9THX 'IJICHOB,,onOpHb1M" 6yaeT TOJIbKO
'IJaeH C S = P. 1H T. a.,OnopHbie '1 ijieHbl pa3JM)1CHH (6.5) 6yJayT TaIKoBbl:
(6.7) (sa - 1) + C is In-1ap P ~ +.~C~j mPE pa PpP?) +
+... + C2 ntp2 P'2 pP2P.
+ ~~& ~ a~ ~l~~P + C,,PkFm-7 aPpp~P +.
n I~~~n