Let K = Z P , F = Z p (x), and E = Z p (x
Question:
Let K = ZP, F = Zp(x), and E = Zp(xP).
(a) F is separably generated and separable over K.
(b) E ≠ F.
(c) F is algebraic and purely inseparable over E.
(d) {xP} is a transcendence base of F over K which is not a separating transcendence base.
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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
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Related Book For
Algebra Graduate Texts In Mathematics 73
ISBN: 9780387905181
8th Edition
Authors: Thomas W. Hungerford
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