If K is an infinite field, and K ( x ) is the field of rational function (in th

Denisse Valdez

Denisse Valdez

Answered question

2022-05-24

If K is an infinite field, and K ( x ) is the field of rational function (in the indeterminate x), is it true that the extension K ( x ) / K is a Galois extension?

Answer & Explanation

Leonard Mahoney

Leonard Mahoney

Beginner2022-05-25Added 10 answers

Since x is not algebraic over K, K ( x ) / K is not an algebraic extension, hence not a Galois extension.

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