If F is a field and a is transcendental over F, prove that F(x) is isomorphic to F (a) as fields.
If F is a field and a is transcendental over F, prove that F(x) is isomorphic to F (a) as fields.
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.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe15b7304-cc73-4505-92c3-23aa2fda4f71%2Fbbfd3129-e5d3-4de4-8fd4-300d5b78d584%2F6znink9_processed.png&w=3840&q=75)
Transcribed Image Text:If F is a field and a is transcendental over F,
prove that F(x) is isomorphic to F (a) as
fields.
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