Proposition. identity on generated fields [1303]
Proposition. identity on generated fields [1303]
Let $\varphi : F(S) \to F(S)$ be a field homomorphism such that $\varphi(\alpha) = \alpha$ for all $\alpha \in F \cup S$. Then $\varphi = id_{F(S)}$.
Let $\varphi : F(S) \to F(S)$ be a field homomorphism such that $\varphi(\alpha) = \alpha$ for all $\alpha \in F \cup S$. Then $\varphi = id_{F(S)}$.