Kitabın içinden
79 sonuçtan 1-3 arası sonuçlar
Sayfa 215
4 and below , we say that g is a normal element of the field F if the additive group
of F is generated by the elements go , o E Aut ( F ) . It is known ( see ( 13 ,
Theorem 2 . 40 ] ) that F always contains a primitive normal element . Lemma 8 .
4 .
4 and below , we say that g is a normal element of the field F if the additive group
of F is generated by the elements go , o E Aut ( F ) . It is known ( see ( 13 ,
Theorem 2 . 40 ] ) that F always contains a primitive normal element . Lemma 8 .
4 .
Sayfa 216
Lemma 8 . 5 . Let g be a primitive element of the field F . Then : ( 1 ) given a EF ,
we have sa · go ] E Orb ( K , T ) for all o E Aut ( F ) whenever ( a · g ] E Orb ( K , 1 )
; ( 2 ) if g is a normal element of F , then ( a · g ) e Orb ( K , I ) for all a € F . Proof .
Lemma 8 . 5 . Let g be a primitive element of the field F . Then : ( 1 ) given a EF ,
we have sa · go ] E Orb ( K , T ) for all o E Aut ( F ) whenever ( a · g ] E Orb ( K , 1 )
; ( 2 ) if g is a normal element of F , then ( a · g ) e Orb ( K , I ) for all a € F . Proof .
Sayfa 217
Let y = a · h be an element of r with nonmaximal a . Then from ( 43 ) it follows that
ag is a maximal element of F , and ( 44 ) ( a · h ) M ( 0 - 9 ) k n ( ag ) K . G = ( ag ·
hg ) M , ( ag · hg ) K ( 0 . g - 1 ) k nak . G = ( a · h ) k , where M is a union of cosets
...
Let y = a · h be an element of r with nonmaximal a . Then from ( 43 ) it follows that
ag is a maximal element of F , and ( 44 ) ( a · h ) M ( 0 - 9 ) k n ( ag ) K . G = ( ag ·
hg ) M , ( ag · hg ) K ( 0 . g - 1 ) k nak . G = ( a · h ) k , where M is a union of cosets
...
Kullanıcılar ne diyor? - Eleştiri yazın
Her zamanki yerlerde hiçbir eleştiri bulamadık.
Diğer baskılar - Tümünü görüntüle
Sık kullanılan terimler ve kelime öbekleri
algebraic analytic apply assume basis boundary bounded called chain homotopy closed coefficients complex computation condition connection Consequently consider constant construction contains continuous convex corresponding defined definition deformation denote determined differential domain element equal equation equivalence estimate example exists extension fact field finite fixed formula function given identity implies inequality integral intersection introduce invariant inverse isomorphism Lemma linear Math Mathematical matrix measure metric Moreover natural normal Observe obtain Obviously operator orientation particular periodic positive present problem projective Proof properties Proposition prove regular relation Remark respectively result ring satisfies scheme sequence singular smooth solutions space standard statement Subsection suffices Suppose takes Theorem theory transformation true twists unique vector weight zero