Frobenius and Quasi-Frobenius Rings

Abstract

The class of rings that are self-injective (as a left or right module over themselves) has been under close scrutiny by ring theorists. There is a vast literature on the structure of self-injective rings satisfying various other conditions. In a book of limited ambition such as this, it would be difficult to do justice to this extensive literature. As a compromise, we focus our attention in this chapter on a special class of such rings called quasi-Frobenius (QF) rings, and the subclass of Frobenius rings. It will be seen that the finite-dimensional Frobenius algebras discussed in §3B are examples of the latter.