Quasi-Frobenius ring

Summary

A quasi-Frobenius ring is a ring that is Noetherian and self-injective on one side; it is then Artinian and self-injective on both sides. Over such a ring a module is projective if and only if it is injective. Frobenius algebras, group algebras of finite groups over fields and the rings $\Z/n\Z$ are quasi-Frobenius. The class generalizes Frobenius algebras from algebras over a field to arbitrary rings.