Quasi-Frobenius ring

This article defines a property of commutative unital rings; a property that can be evaluated for a commutative unital ring
View all properties of commutative unital rings
VIEW RELATED: Commutative unital ring property implications | Commutative unital ring property non-implications |Commutative unital ring metaproperty satisfactions | Commutative unital ring metaproperty dissatisfactions | Commutative unital ring property satisfactions | Commutative unital ring property dissatisfactions

Definition

A commutative unital ring is termed quasi-Frobenius if it satisfies the following equivalent properties:

• It is injective as a module over itself
• Every projective module over it is injective
• Every injective module over it is projective

Relation with other properties

Stronger properties

• Field
• Semisimple Artinian ring