Let $F$ be a field and $L_1$, $L_2$ two subfields such that $F$ is finite over both $L_1$ and $L_2$. Is $F$ necessarily finite over the intersection $L_1 \cap L_2$?
2026-04-23 01:41:19.1776908479
If $F$ is finite over $L_1$ and $L_2$, is it also finite over $L_1 \cap L_2$?
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