Let $F\subset L$ be a field extension, and $x,\alpha,\beta\in L$.
My question is:
Assume that $F(\alpha)\subset L$ is an algebraic extension. If $\alpha$ is algebraic over $F(\beta)$, then is $x$ algebraic over $F(\beta)$?
Thank you.
2026-04-08 11:00:06.1775646006
A generator which is algebraic
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