Definition:Separably Closed Field

From ProofWiki
Jump to navigation Jump to search


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 $K$.

Also see