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I'm currently reading the paper of Henri Cohen & Jacques Martinet "Etude heuristique des groupes de classes des corps de nombres" On the 2nd section, they recall some facts on valuations, ...

Luroth's theorem states that if $k$ is a field and $L$ is a field extension of $k$ such that $k \subset L \subseteq k(X)$, then $L=k(f(X))$ for some $f(X) \in k(X) $ . My question is ; is there any ...