Osnovy teorii Galua.

108 I11. Pappewuuvue ypaonernti
fIOJHHOMOB Xrn -1 coaep>Kaag~x MHO)KHTeJnb x -a. fiPH 9TOM Ka1I(AbIlft
fIOJIHHOM Xm, - 1 aeaJHTCHi TOJ~bKO Ha HepBYIO CTeHeHb X -6,5 TaK lKaK
xl~- I Boo6ume He COJLePWHT KpaTHbIX K(OpHefl. B camom jAeie, fIpOH3BOAHaR
OT Xrni -1paB~a m1 Xmlll 1T. e. Oqei1UaHO B3aiMHO-rnpOCra c xrnm-1
TaKtim o~pa3oM q~icnio (2.4) yKa3bIBaeT, CKOJnbKO paa MHO}KHTe1b x-
BXOAHT B 4IICJHT6J~b Bbipa}KeHH51 (2.3).
Paccywjxa5 alaJIorHLIHo, Hafl~em, 'iro i 3HaMeHaTeJnb BblpaxmeHHHn (2.3) mHo)KHTeJlb X- E BOR~JeT
(2.5)Ct Ct k Cj+ p3
Pa3HOCTI, lHceJI (2.4) H (2.6) paB~a
1 -Ckl + Ck _C. c+ Ck4.. (...l
T. e. HyqJix~ aw1ubif pa3, Koraia k > 0, Hi paBna e1m1HtIxe npip k =0. TalcuM
o(Spasom MHO)KHTeJ1b x -~ B0oDaeT B Bb1pa)KeHHe (2.3) ior.Lta H TOJqbK0,.
Tor~raa, ecnti k = 0, T. e. eCJiH d 1-M, T. e. e 0CTb nepBoO6pa3Hblil M-t
KOpeHb, H B 3TOM Caiyqae x - s BotlJaeT 0)UIH pa3. 3TO A0Ka3bJBaeT cupaveJ[JHB0CTb 4)OPMy.3bz (2.3).
fPHum e p. Onpeale.uIm X630. 143 4)opMy~ibl (2.3) ca~eayeT, 'ITO
=(XOI i )(xiQ~ i )(x-I 1)(x' -.1)
XAeAi O1AHH Ha A~pyroft MWo'4HTen ii, CTOguUtie OJUHH Hua. JpyrHim,flony'iHm.(X@t+ 1)(:t2+ 1) - 2 ~- x9o+ 1 x16 + X14 - Xl0-X8l-X6+Xl+
Xe.- (X'~ +1)(X+1 -X4-'-X +1
C A~ e A C T B ii e. Creneib floJHHoma X. paBHa Tp(M), T. e. 'IMCArY 1Hceqi,
He flpeBbIUaI~lONiX M Hi B3aHMHo-nIpocTbIX C M.
2. Ta6Au1ja UOAHHOMOB X.JAO mn = 60. HlpHBeJaeM Bb1paxKeHHHl FIOJHHOMOR
Xm Anl~ qHiceaT mf, He npe~BbIlwaLoutHx 60. fHpH STO1M MI He, 6y~em HPHBO)kHTb X., HpH npoCTblx 113, TOK Ha(K B 3TOM ciiyqae IIPOCTO
(2.6) Xm - o XM1+Xi2 n- +X
a TaK)Kt xQVr~ m = 2 p, He'ieTHoe npocroe qHuCa~o, TaK 1a2K B n'om
cny'iae
2.7) xv p -( 1 = X- +1I XV-1-Xy 2 + Xp3..+
Xff (X-P ~ X 4 1
+ xt- X+ 1