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 öme larger field. If K is a Galois xtension of F then KE is a Glois extension of E and G(KE, E)=G(K,KNE).|
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 öme larger field. If K is a Galois xtension of F then KE is a Glois extension of E and G(KE, E)=G(K,KNE).|
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.3: Factorization In F [x]
Problem 16E
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![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,KNE).|](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F49b049d7-ccdc-43a8-b3ca-38ba2fb8bbab%2F1eb511f5-6d9f-43a4-a1ef-fd793cc7102c%2F2pjtvu_processed.png&w=3840&q=75)
Transcribed Image Text: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,KNE).|
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