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 separable1 over $F$ if every element of $K$ is separable over $F$.