Let F be a eld of characteristic p > 0. Let a EF be such that ais not a pth power of any elementof F. Show that xP-a is irreducible over F.

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Answered: Let F be a eld of characteristic p > 0.…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter8: Polynomials

Section8.4: Zeros Of A Polynomial

Problem 33E: Let where is a field and let . Prove that if is irreducible over , then is irreducible over .

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Let F be a eld of characteristic p > 0. Let a EF be such that ais not a pth power of any element of F. Show that xP-a is irreducible over F.