Let E be an intermediate field. (a) If F is algebraic Galois over K, then F is

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Let E be an intermediate field.

(a) If F is algebraic Galois over K, then F is algebraic Galois over E. show that the "algebraic" hypothesis is necessary.

(b) If F is Galois over E, E is Galois over K and F is a splitting field over E of a family of polynomials in K[x], then F is Galois over K.

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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 16, 2023 03:50 AM

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Let E be an intermediate field. (a) If F is algebraic Galois over K, then F is

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a The algebraic hypothesis is necessary Suppose that F is algebraic Galois over K but not algebraic Galois over E This means that there exists an elem...View the full answer

Algebra Graduate Texts In Mathematics 73

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