Let F( 1 , , n ) be an extension field of F. Show that
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Let F(α1, · · ·,αn) be an extension field of F. Show that any automorphism σ of F(α1, · · ·,αn) leaving F fixed is completely determined by then values σ(αi).
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We proceed by induction on n For n 1 Corollary 485 shows that is completely determined by 1 which mu...View the full answer
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