Finite 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 finite if it satisfies the following equivalent conditions:

1. The underlying set of the field is finite.
2. The underlying set of the field has size equal to a power of a prime.
3. The underlying set of the field is a finite extension of a finite prime field.

Relation with other properties

Stronger properties

• Finite prime field

Weaker properties

• Field of prime characteristic
• Finite extension of prime field
• Normal extension of prime field