Osnovy teorii Galua.

182

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+ Sk = ) TO rpynnfa rajiya ypaBHeHH54 (4.2) COJLep>KHT noJaCTaHoBI<y,
COCTOR111LIO 143 IIHKJOB T1OPHRLKOB S1, S2,...,- Sk.
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ucero MO>KHo 6biao 6Mi XOKa3aTb, 4TO COBOK~rHHOCTb p-aR~4eCKHX pSIAoB
COCTaBaRIeT none. HO3TOMy eCaHn Mbl BKJIIO'IHM B o6naCmb paixiOH 'anbHOCT1{
p-a~aH~eCKHe ps1Jabi no 1LeJab1m CTnHfHS1M p, a TaKM(e HeKOTOpbie pt-bie KOPHH
113 eJHHHU~bl, TO cmo}Kem oflpeJLeJHTb rpynriy ranya xIqm TaKOR1 06.naCTx
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cylCB~B~ COOTHOiueHHHl me)KJy KOPHRIMH coxpaH5IfOTCfI, TO MO)KHO
AtOKa33Tb (C.p. )ToKa3aTeJIbCTBO Teopembi 90), 'ITO rnpH 3TOm rpyniia [ranya
6yaLeT H30Mopt43Ha c J~eaHTeJIem HepBoHatiaJqbHofl rpynni ra~nya.
Tenepb HOCTPOHm npOH3BO2J5]I1yto nOJCTaHOBKY rpynribi raniya ypaBHeHH4,9
(4.2) B p-aJLH'eci~ofl o6AaCTi- paLLioHa.RbHocTH. V]YCTb s 6yJaeT -o6nmee
2nit
HaHmeHbweeC KpaT~oe 1-4tceJi SI, S,.., SO, i4 a = e 8 - epBoo6pa3Hbffl S-it.,KopeHb 143 eAHHH1Th1. ECnHi Mbl BO Bcex p-aawqeCKIIX pa3Io)KeuwiIX KopHehk
ypa]3HeHHH~ (4.2) 3ameHHM BeJ1H'HHp p8 qepe3 PEP8 TO Bce ILHKJlbI, KOTopbWe
o6pa3y lOT 9TH pa3Jlo)eHHI, Hpei'epni5T LLKiH4eCKoe nepementel-i~e BXOJU11IUHX
i HHX pa3Jlo)KenHf Ha O)UHH muar. TaKHM o6pa3oM noJ1y'iHTCR noJaCTaHoBKa,
COCTO14faLg 13 U1HKJ1OB nOPRA1KOB SI, S21.. Sk. 3Ta nI0JCTaHOBKa He moIKOT
mapy1lUHTb COOTHOweHH4A me)KJL KopH51MH. B camom aenie, ypaBi-eHife
Z -p =, KaK MO)KHo 6bL110 6b1 n~oiaaTb, HenpH4BOAH4MO )ia3)e B HameR
paCWlHpeHHOfl o6nacTH paLLHoHaJ~bHoCTH, a n1OTOMY BO BCSIKOM COOTHOIIIHH14
me)KLLy ero KOPH51M4 P, p8, p~s)0.81 P8 MO)KHO Bcerjaa 3aMHHTI4T
p S epe3 ep 8. BmeCTe C Tem mb! mo>Kem pacaP~~ COOTHoHweHHfi me)KJJy
KOPHSIMH ypalBHeHHH (4.2) B pacHJmpeHHOI4 o6.naCTH p3LHOHaJlbHOCTH4 KaK
COOTHOUIHCHH5 meWKJ1 KOPHRMH ypaBHeHH51 Z'-p = 0.
143 9TOf Teo1pembl HeriocpenACTeH110 BbMTeKaeT
T e 0 p e M a 95. ECnrm KOPHH aare6pawiqecKoro ypaBHeHH xtonyc-.
KaIOT p-3A~u4ecKtie pa3Ao>KeH~s no Jipo6HuTM CTenHFHIM npoc~oro HqHCj1a
p, RpH'ie noKa3aTenui p co~ep)KaT B 3HaMeHarejisiX qHCnTo S, To nopsiALLK rpynni Fa~nya 3Toro ypaBHeHH11 J1ie1HTC Ha s.
Y ni p a )K H4 e H H e 43. faOKa3aTb npaBBHJIbI10CTh 2-aRu'IecKoro pa3J1o)KeHl51
3
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Tomjt H TOJlIbKO Tm~a, ecJ1H npeaCraB~lwjemoe 3THM Pa3JoxceHHem IHcJIo paIuIoHaJlbHO.
Y1 i p a mc H e H H e 45. HAfTH Ha'Ianibliwe 'uxeubl pa3nwoKeHMHi B pixaIHqecKme 1psu~b
Kcopeeli ypaBnenHfl, YAOBaeTBOPHIO1JaHX YCJIOBHBM KPHTepH11 9AR3eHWTefiHa AJIA
Toro rae p.