Let K be a field estension of a field Fand let a1, a2,.....an be elements in Kwhich are algebric over F. ThenF(a1, a2.......an) is a finite extension ofF and hence an algebric extension of F

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Answered: Let K be a field estension of a field F…

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 18E: 18. Let be the smallest subring of the field of rational numbers that contains . Find a...

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Let K be a field estension of a field F and let a1, a2,.....an be elements in K which are algebric over F. Then F(a1, a2.......an) is a finite extension of F and hence an algebric extension of F