Separably closed field

This article defines a field property: a property that can be evaluated to true/false for any field.
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Definition

A field is termed separably closed if it satisfies the following equivalent conditions:

1. Every irreducible polynomial over it that is separable is linear.
2. It has no proper algebraic extension that is separable.

For any field, we can define the separable closure of the field, which is the unique smallest separably closed field containing it.