A Generalization of Continuous Modules and Their Application to QF-rings

Abstract

A ring R is called quasi-Frobenius, briey QF, if R is right or left artinian and right or left self-injective. In this note we study the new class of modules which generalize the concept of continuous (quasi-continuous) modules, that is, ec-continuous (ec-quasi-continuous) modules. We prove the decomposition theorems for ec-quasi-continuous modules, and we also give a sufficient condition for ec-continuous to be continuous. Moreover, we give a characterization of QF-rings with the injectivity condition replaced by ec-continuity.