I am trying to show that a finite extension $B/F$ has an extension $E/F$ such that $E/F$ is the splitting field of some $f(x)\in F[x]$.
I have trouble seeing where to begin with this problem.
2026-04-13 00:48:23.1776041303
A finite extension has a splitting field extension
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Hint. Consider $b_1,\dots,b_m$ generators of $B/F$ and $f$ the product of their minimal polynomials.