Let F be a field and E an extension field of F that contains a1,a2, . . . , an. Prove that F(a1, a2, . . . , an) is the intersection of allsubfields of E that contain F and the set {a1, a2, . . . , an}.

Let F be a field and E an extension field of F that contains a1,a2, . . . , an. Prove that F(a1, a2, . . . , an) is the intersection of allsubfields of E that contain F and the set {a1, a2, . . . , an}.

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter1: Fundamentals

Section1.5: Permutations And Inverses

Problem 5E: Let f:AA, where A is nonempty. Prove that f a has right inverse if and only if f(f1(T))=T for every...

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Question

Let F be a field and E an extension field of F that contains a1,
a2, . . . , an. Prove that F(a1, a2, . . . , an) is the intersection of all
subfields of E that contain F and the set {a1, a2, . . . , an}.

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