On a generalization of cofinitely lifting modules

Abstract

In this paper, we study on cofinitely Rad-lifting modules as a proper generalization of modules with the property (P?) and cofinitely lifting modules, and we obtain the properties of these modules. In particular, we prove that if M with the property (SSP) is a cofinitely Rad-lifting module, then M/N is a cofinitely Rad-lifting module for every direct summand N of M. We show that ?-projective cofinitely (Rad-) ?-supplemented modules are cofinitely (Rad-) lifting. We obtain a new characterization of semiperfect rings by using this result. This characterization generalizes the result of Wang and Wu. © 2014 Academic Publications, Ltd.