Definition:Separably Closed Field

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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 $K$.


Also see