Perfect field

This article defines a field property: a property that can be evaluated to true/false for any field.
View a complete list of field properties|View a complete list of field extension properties

Definition

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

1. It is either a field of characteristic zero or it has characteristic $p$ for some prime $p$, and the Frobenius map is surjective.
2. Every finite extension of the field is a separable extension.
3. Every irreducible polynomial over the field is a separable polynomial.

Equivalence of definitions

Further information: Equivalence of definitions of perfect field

Relation with other properties

Stronger properties

• Algebraically closed field
• Field of characteristic zero
• Finite field