Let K[x] is the polynomial ring over the field K be a field and let F be a subfield of K. If F is a perfect field and f(x) in F[x] has no repeated irreducible factors in F[x]. Prove that f(x) has no repeated irreducible factors in K[x].

Let K[x] is the polynomial ring over the field K be a field and let F be a subfield of K. If F is a perfect field and f(x) in F[x] has no repeated irreducible factors in F[x]. Prove that f(x) has no repeated irreducible factors in K[x].

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 16E

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