et K and E be the extension of a field F with [K:F] finite and assume that both K and E are subfields of some larger field. If K is a Galois extension of F then KE is a Glois extension of E and G(KE, E)≅G(K,K∩E).

et K and E be the extension of a field F with [K:F] finite and assume that both K and E are subfields of some larger field. If K is a Galois extension of F then KE is a Glois extension of E and G(KE, E)≅G(K,K∩E).

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.1: Ideals And Quotient Rings

Problem 35E: Let R be a commutative ring with unity whose only ideals are {0} and R Prove that R is a...

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Question

Let K and E be the extension of a field F with
[K:F] finite and assume that both K and E are
subfields of some larger field. If K is a Galois
extension of F then KE is a Glois extension of
E and G(KE, E)≅G(K,K∩E).

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