If F is a field and a is transcendental over F,prove that F(x) is isomorphic to F (a) asfields.

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Answered: If F is a field and a is transcendental…

Elements Of Modern Algebra

8th Edition

ISBN:9781285463230

Author:Gilbert, Linda, Jimmie

Publisher:Gilbert, Linda, Jimmie

Chapter6: More On Rings

Section6.3: The Characteristic Of A Ring

Problem 18E

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If F is a field and a is transcendental over F, prove that F(x) is isomorphic to F (a) as fields.