Osnovy teorii Galua.

II. rpynna raaya

7. PaCCMOTpH4M cJay'iar, ioraa HeKOTopLJ 113 BeJ1HxHH I?(0) (i=1,..
-paBmbi 31pyr jipyry. H1YCTb
13 TO Bpem51 KaK OCTaJ~bHbie BeHCJIH'HUb (0?) (i " + 1,. nf) He paBHb1.R (Os). Toraa nIoJi4HOM (3.4) paiieH- MA- CTe1ieHH HeOKOTOpor'O HenpHIBOJLH -
mocro nlOi HHoma h (t). B camom ateuTe, flyCTb h (t) 6yxaeT HenpHBOJ1Hmbifl noJIFIHOM, KOTOpb1fl HmeeT 1COPHeM ~. Toraia OLIeBHRJHO, 14TO g(t) JIeJHTCSI TO'IHO
Ha. m-io CTeneH b h (t) (Teopema 44). HOJoKmmi g (t) = [Ih (t)]9 g, (t), rjc
g,(t) B3aHmHo TIpOCTOR1 C hz(t) HOATHHOM. 1o2Ka}Kem, 'ITO gj (f)-noc1.To0AHna5.Be uquna. TJIOVyCTHB HpOTHBHoe, 6yaeM B CiHiY 4~OPMYJlbl (1w3~) leTb:
r~e 11t Ii V (t)-no.TrnHoMbl. fHOJCTaBni5151 t R(X), Io~nyqiu4M:
BmeCTC C TeM g1 (t) HmeeT B CWT1Y (3.4) KopeHb I,,l1aa ~ B clu1y
uero paUyloHan1Haq q)YHKlUMI (Boo6nte FOBOP51 Itpo6Hasi) g, [R(X)J ic0Ai}1Ha
I4meTb B 'IHCJIHTeJIe HOIIHOM, Hmeo1IHA c f (x) o6nut1 icopem Q, 14i r11TOMY
B cHJIy HeHR14BOAitMOCTI 1(X) H Teopembi 44 aeisiuMHcOI uHa f (x). B city
3T0F0 g, [R "Q)] 0 (i = 1, 2,, n). TotIHO Talc )Ke Jocalwem, 'ITO
h [1? (%)1 0 (i =1, 2,.. n'). F10,CcTaB.lwi 13 (3. 5) x Q.rioj-!yql'M 0 =1
T,. e. rHpOTHBopeu1Fe. OTCioaa 3aL(JL aei:
Teo p e ma 48. Ec~im OP 02 2'~' Iit — Ko~ HernpHBOJL1MoI'o no0111 -iioma f (x), a R? (x) - pa1Xuoi1A.TbHa1R (~yHKLtU4 (3ria-,.eilaTeJnb icompOil
ii0 e TieiMTCSI Ha 1(x)), TO nIO JHOM
(tR-I (01)) ( -~ RI 024).. (t-R,EC "Ib C TeI71Hb HerlpHB3OLLMOI'O HORTiHHoma.
B Cgiyqaa- III>I Bien iwiua I?(% POM3BOJ1T He Bce non'e,
a TOibRo ero Hacfb, AI~I, maiCMbi16y;,iOmfrOBOp11Tb, a e 14 TeJb HO 3151.
8. T c o p e m a 49. Ecuw 0 Hn14MHTIMB13bIft 3J1eMeHT HOJIS CTeneHHII U1,
TO BCR11Ht1 3JemeHT -3T0P0 rioJW m0K110 -1npeLCT,'1BHTb B MaeJ~ HohIHoma
C TeJimli He B~bJill n - 1:
eeo Ch(dprbiHeuIOHbi (to, Ci.1.,__ paLLHOHaaTbHbie 'JIcJna. 3TO npexaC Ta3jieHHe ejHHCTBeHF1oc.
}i O a3aTeJnbCTBO. 10. I1ycTb memeMHT MOISI 3aJ1aH B BHLLO ( =
rXte r~ (x) IiM x B3a1IMH0-Hp0CTbie 13011313MbI (imatie,po6b MO)KHo 6b111o
6ul COKpaTHIb). HlOJItHOM r~(x) )TO eiiO 6b1Tb B33131MH0 HpOCTb1M C f(X), TaK
KaK HHaHe 3HaMeHaTOJb xcpofi o6palua1cq 6Nl B Hy~ib, Hi apo6b HmOna. 6bi
-6ecKOHe'qiHoe Maqaemue. HO03TOMy 14 B CH1R d~opmyjuim (1.3") IHMeeT meCTO
II (xf(x) + v Wx) ~(X) -