Let E be a finite extension of a field F, and let p(x) F[x] be irreducible

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Let E be a finite extension of a field F, and let p(x) ∈ F[x] be irreducible over F and have degree that is not a divisor of [E : F]. Show that p(x) has no zeros in E.

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A First Course In Abstract Algebra

ISBN: 9780201763904

7th Edition

Authors: John Fraleigh

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Question Posted: Jan 09, 2023 01:44 AM

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Let E be a finite extension of a field F, and let p(x) F[x] be irreducible

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If a zero of px were in E then because px is irreducible over F we would have F F degpx and F F woul...View the full answer

A First Course In Abstract Algebra

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