If x n - a K[x] is irreducible and u F is a root of

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If xⁿ - a ϵ K[x] is irreducible and u ϵ F is a root of xⁿ - a and m divides n, then prove that the degree of u^m over K is n/m. What is the irreducible polynomial for u^m over K?

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 16, 2023 03:50 AM

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If x n - a K[x] is irreducible and u F is a root of

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Since xn a is irreducible and u is a root we have KuK n Also since m divides n we have n mk for some ...View the full answer

Algebra Graduate Texts In Mathematics 73

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