Let char K p 0 and let u be transcendental over K Suppose F is generated over K by u,v 1 ,v 2 , , where v i is a root of x pi u K(u) x for i 1,2, Then F is separable over K, but F is not separably generated over K ...

Let me explain the given description in detail Given K is a field with characteristic K 0 u is a tra ...

Let char K = p 0 and let u be transcendental over K. Suppose F is

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Let char K = p ≠ 0 and let u be transcendental over K. Suppose F is generated over K by {u,v₁,v₂, ... } , where v_i is a root of x^pi - u ϵ K(u)[x] for i = 1,2, .... Then F is separable over K, but F is not separably generated 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 20, 2023 02:59 AM

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Let char K = p 0 and let u be transcendental over K. Suppose F is

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Algebra Graduate Texts In Mathematics 73

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