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!