I have seen this claim multiple times, but every time I read a proof, the first step is to find the minimal polynomial for an element of the field and use its irreducibility to show separability. However, is this not assuming that the field extension is algebraic? Are there non-algebraic extensions of say $\Bbb Q$ that are not separable?
2026-05-15 08:19:10.1778833150
Are all extensions of fields of characteristic $0$ separable?
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