Prove if 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).

Prove if 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).

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Question

Prove if 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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Please solve as soon as possible
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).
Unless otherwise stated, F is a field. V , W, and X are vector spaces over F.
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