Please fast If E is an extension of F and f (x) e F[x] and if o isan automorphism of E leaving every element of F fixed, prove that ¢ musttake a root of f (x) in E into a root of f (x) in E.

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Answered: If E is an extension of F and f (x) e…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.2: Integral Domains And Fields

Problem 16E: Prove that if a subring R of an integral domain D contains the unity element of D, then R is an...

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If E is an extension of F and f (x) e F[x] and if o is an automorphism of E leaving every element of F fixed, prove that o must take a root of f (x) in E into a root of f (x) in E.