(a) If u 1 , ... , U n E Fare separable over. K, then K(u 1...

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(a) If u₁, ... , U_n E Fare separable over. K, then K(u₁, ... , un) is a separable extension of K.

(b) If F is generated by a (possibly infinite) set of separable elements over K, then F is a separable extension of 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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(a) If u 1 , ... , U n E Fare separable over. K, then K(u 1...

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Proof a Let L Ku1 un Since each ui is separable over K we know that KuiK degmi for some irreducible ...View the full answer

Algebra Graduate Texts In Mathematics 73

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