If u,v F are algebraic over K of degrees m and n respectively, then [K(u,v) :

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If u,v ϵ F are algebraic over K of degrees m and n respectively, then [K(u,v) : K] ≤ mn. If (m,n) = 1, then [K(u,v) : K] = mn.

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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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If u,v F are algebraic over K of degrees m and n respectively, then [K(u,v) :

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The field extension Kuv over K is generated by u and v so any element of Kuv can be expressed as a p...View the full answer

Algebra Graduate Texts In Mathematics 73

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