LEC ALG4 16

Let $F$ be a field. Fix an algebraic closure $\overline{F}$ of $F$.

[!Definition]
Let $\alpha \in \overline{F}$. Say that $\alpha$ is separable over $F$ if the minimal polynomial $m_F(x)$ of $\alpha$ over $F$ has distinct roots in $\overline{F}$.