Q. Theorem 6. Let K be a field extension of a field F and let a,, a,., a, be elements in Kwhich are algebric over F. Then F (a,, a,.., a,) is a finite extension of F and hence an algebric exten-sion of F.

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Answered: Theorem 6. Let K be a field extension…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter5: Rings, Integral Domains, And Fields

Section5.3: The Field Of Quotients Of An Integral Domain

Problem 13E

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Theorem 6. Let K be a field extension of a field F and let o which are algebric over F. Then F (a,, a,., a,) is a finite extension of sion of F.