Definition 9.12.2. Let $F$ be a field. Let $K/F$ be an extension of fields.

We say an irreducible polynomial $P$ over $F$ is

*separable*if it is relatively prime to its derivative.Given $\alpha \in K$ algebraic over $F$ we say $\alpha $ is

*separable*over $F$ if its minimal polynomial is separable over $F$.If $K$ is an algebraic extension of $F$, we say $K$ is

*separable*^{1}over $F$ if every element of $K$ is separable over $F$.

## Comments (2)

Comment #4936 by Laurent Moret-Bailly on

Comment #5202 by Johan on

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