03 February 2022 0 8K Report

Let C denote the field of complex numbers and let C(x) denote the field of rational functions over C, with variable x.

I know that C and C(x) are isomorphic. Can one give a reference for the proof?

Regarding this question, let F denote any field and let F(x) denote the field of rational functions over F, with variable x.

Under what conditions on F, F(x) and F are isomorphic?

Can one give a reference for that?

Many Thanks And All The Best!

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