Answered: Let f (x) be a cubic irreducible over…

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

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

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