Definition:Separably Closed Field

Definition

Let $K$ be a field.

Then $K$ is separably closed if and only if

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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

Sources

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