Let K Z P , F Z p (x), and E Z p (x P ) (a) F is separably generated and separable over K (b) E F (c) F is algebraic and purely inseparable over E (d) x P is a transcendence base of F over K which is not a separating transcendence base ...

a F is separably generated and separable over K To show that F is separably generated over K we need to show that there exists a set S of elements in F such that F is the separable closure of KS in F ...

Let K = Z P , F = Z p (x), and E = Z p (x

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Let K = Z_P, F = Z_p(x), and E = Z_p(x^P).

(a) F is separably generated and separable over K.

(b) E ≠ F.

(d) {x^P} is a transcendence base of F over K which is not a separating transcendence base.

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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 20, 2023 02:59 AM

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Let K = Z P , F = Z p (x), and E = Z p (x

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a F is separably generated and separable over K To show that F is separably generated over K we need to show that there exists a set S of elements in F such that F is the separable closure of KS in F ...View the full answer

Algebra Graduate Texts In Mathematics 73

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