(a) Let c F, where F is a field of characteristic p (p prime). Then x...

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(a) Let c ϵ F, where F is a field of characteristic p (p prime). Then x^P - x - c is irreducible in F[x] if and only if x^p - x - c has no root in F.

(b) If char F = 0, part (a) is false.

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Algebra Graduate Texts In Mathematics 73

ISBN: 9780387905181

8th Edition

Authors: Thomas W. Hungerford

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Question Posted: Apr 15, 2023 03:05 AM

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(a) Let c F, where F is a field of characteristic p (p prime). Then x...

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a Let fx xP x c and suppose fx is irreducible in Fx Then by the factor theorem fx has no roots in F ...View the full answer

Algebra Graduate Texts In Mathematics 73

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