Applications of Epi-Retractable and Co-Epi-Retractable Modules

Abstract

A module M is called epi-retractable if every submodule of M is a homomorphic image of M. <br />Dually, a module M is called co-epi-retractable if it contains a copy of each of its factor modules. In special case, a ring R is called co-pli (resp. co-pri) if RR (resp. RR) is co-epi-retractable. It is proved that if R is a left principal right duo ring, then every left ideal of R is an epi-retractable R-module. A co-pli strongly prime ring R is a simple ring. A left self-injective co-pli ring R is left Noetherian if and only if R is a left perfect ring. It is shown that a cogenerator ring R is a pli ring if and only if it is a co-pri ring. Moreover, if R is a left perfect <br />ring such that every projective R-module is co-epi-retractable, then R is a quasi-Frobenius ring.