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 um over K is n/m. What is the irreducible polynomial for um over K?
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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
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Deepak Sharma
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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