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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Question
Let f (x) be a cubic irreducible over Zp, where p is a prime. Prove
that the splitting field of f (x) over Zp has order p3 or p6.
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