Suppose [F : K] is finite. Then the following conditions are equivalent: (i) F is Galois over

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Suppose [F : K] is finite. Then the following conditions are equivalent:

(i) F is Galois over K;

(ii) F is separable over K and a splitting field of a polynomial ∫ ϵ K[x];

(iii) F is a splitting field over K of a polynomial ∫ ϵ K[x] whose irreducible factors are separable.

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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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Suppose [F : K] is finite. Then the following conditions are equivalent: (i) F is Galois over

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These conditions are equivalent by the fundamental theorem of Galois theory Heres a brie...View the full answer

Algebra Graduate Texts In Mathematics 73

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