17. If E is an extension of F and f (x) e F [x] and if 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.
17. If E is an extension of F and f (x) e F [x] and if 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.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter6: More On Rings
Section6.1: Ideals And Quotient Rings
Problem 24E: 24. If is a commutative ring and is a fixed element of prove that the setis an ideal of . (The set...
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