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Let f (x) be a cubic irreducible over Z2. Prove that the splitting fieldof f (x) over Z2 has order 8.

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 3E: Find all monic irreducible polynomials of degree 2 over Z3.

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Question

Let f (x) be a cubic irreducible over Z₂. Prove that the splitting field
of f (x) over Z₂ has order 8.

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