Quasi-coretractable modules

In this paper, we will discuss and study the structure of quasi-coretractable modules. Some characterization theorems of quasi-coretractable modules in terms of Kasch rings, CS modules, mono-coretractable modules, projective modules, epi-retractable modules and retractable modules will be given. Some equivalent conditions related with the quasi-coretractable and the mono-coretractable module will also be considered and investigated. Some recent results given by Singh on coretractable modules will be extended and enriched.

SOME RESULTS ABOUT CORETRACTABLE MODULES

Throughout this paper, all rings have identities and all modules are unitary right modules. Let R be a ring and M an R-module. A module M is called coretractable if for each proper submodule N of M, there exists a nonzero homomorphism f from M/N into M. Our concern in this paper is to develop basic properties of coretractable modules and to look for any relations between coretractable modules and other classes of modules.