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# Let f (x) and g(x) be irreducible polynomials over a field ## Problem 32E Chapter 21

Contemporary Abstract Algebra | 8th Edition

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Problem 32E

Let f (x) and g(x) be irreducible polynomials over a field F and let a and b belong to some extension E of F. If a is a zero of f (x) and b is a zero of g(x), show that f (x) is irreducible over F(b) if and only if g(x) is irreducible over F(a).

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##### ISBN: 9781133599708

This full solution covers the following key subjects: irreducible, Zero, let, Field, extension. This expansive textbook survival guide covers 34 chapters, and 2038 solutions. This textbook survival guide was created for the textbook: Contemporary Abstract Algebra , edition: 8th. Since the solution to 32E from 21 chapter was answered, more than 223 students have viewed the full step-by-step answer. Contemporary Abstract Algebra was written by Sieva Kozinsky and is associated to the ISBN: 9781133599708. The answer to “Let f (x) and g(x) be irreducible polynomials over a field F and let a and b belong to some extension E of F. If a is a zero of f (x) and b is a zero of g(x), show that f (x) is irreducible over F(b) if and only if g(x) is irreducible over F(a).” is broken down into a number of easy to follow steps, and 56 words. The full step-by-step solution to problem: 32E from chapter: 21 was answered by Sieva Kozinsky, our top Math solution expert on 07/25/17, 05:55AM.

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