Quasi-c-Principally Injective Modules and Self-c-Prin-cipally Injective Rings

摘要

In this paper, the concepts of quasi-c-principally injective modules (in short,quasi-cp-injective modules) and self-c-principally injective rings are introduced. Insupport of these concepts we have also provided the examples. The characterizationand some properties of quasi-cp-injective modules are given in terms of their endo-morphism rings. The characterization of self-c-principally injective rings is given interms of annihilator ideals. Apart from this, the characterization of semi-simple ar-tinian rings is given in terms of quasi-cp-injective modules. Sufficient conditions aregiven for quasi-cp-injective modules to become co-Hopfian and weakly co-Hopfian. Inthe begining of this paper we have introduced M-c-principally injective modules for aright R-module M and have studied their properties. The examples of M-cp-injectivemodules are given, which are not M-principally injective modules and M-c-injectivemodules, respectively.