Let K be the splitting field of a separable, irreducible polynomial f E F[x], and suppose Gal(K/F) is abelian.Let a e K be a root of f. Show that F(@) = K.%3D

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Let K be the splitting field of a separable, irreducible polynomial f € F[r], and suppose Gal(K/F) is abelian. Let a e K be a root of f. Show that F(@) = K. %3|

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 K be the splitting field of a separable, irreducible polynomial f E F[x], and suppose Gal(K/F) is abelian.
Let a e K be a root of f. Show that F(@) = K.
%3D

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