# Definition:Separably Closed Field

## Definition

Let $K$ be a field.

Then $K$ is separably closed if and only if

### 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 $K$.