Let F be a field of characteristic p and let f (x) = xp - a ∈ F[x]. Show that f (x) is irreducible over F or f (x) splits in F.
Let F be a field of characteristic p and let f (x) = xp - a ∈ F[x]. Show that f (x) is irreducible over F or f (x) splits in F.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 8E: Let be an irreducible polynomial over a field . Prove that is irreducible over for all nonzero ...
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Let F be a field of characteristic p and let f (x) = xp - a ∈ F[x]. Show that f (x) is irreducible over F or f (x) splits in F.
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