If K is a field extension of F and $S\subseteq K$ is such that each s in S is F-algebraic, is it true that F[S] = F(S)?
If $K$ is a field extension of $F$ and $S \subseteq K$ is such that each $s \in S$ is $F$-algebraic, is it true that $F[S] = F(S)$?
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field-theory
galois-theory