Characterization of rings using finite-direct-injective modules

Abstract

In this paper, we characterize strongly right C2-rings in terms of finite-direct-injective modules which is a generalization of direct-injective modules (or C2-modules). Using this result, we give an example of a finite-direct-injective module which is not a direct-injective module. We prove that if every finite-direct-injective right R-module is a direct-injective module, then the ring R must be right Noetherian. Also, we characterize semisimple artinian rings, regular right FGC-rings in terms of finite-direct-injective modules. © 2020 World Scientific Publishing Company.