Let $L/F/K$ is a tower of field extensions. Let $a\in L$. If $F/K$ is an algebraic extension of fields, is $F(a)/K(a)$ still an algebraic extension of fields?
2026-04-05 18:35:49.1775414149
Algebraic extension of fields
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Yes, $F(a)=K'(F)$ for $K' = K(a)$ and every element of $F$ is algebraic over $K$, so also over $K'$.