Definition:Separably Closed Field

Definition
Let $K$ be a field.

Then $K$ is separably closed

Definition 1
The only separable field extension of $K$ is $K$ itself.

Definition 2
Every separable irreducible polynomial over $K$ has degree $1$.

Definition 3
Every separable polynomial over $K$ of strictly positive degree has a root in $K$.

Also see

 * Equivalence of Definitions of Separably Closed Field
 * Definition:Perfect Field, a field with no inseparable extensions
 * Definition:Algebraically Closed Field