Endomorphism Ring of Quasi-rp-injective and Quasi-lp-injective modules

Abstract

Let R be a ring. A right R-module N is called an M-p-injective module if any homomorphism from an M-cyclic submodule of M to N can be extended to an endomorphism of M. Generalizing this notion, we in- vestigated the class of M-rp-injective modules and M-lp-injective mod- ules, and proved that for a finitely generated Kasch module M, if M is quasi-rp-injective, then there is a bijection between the class of maximal submodules of M and the class of minimal left right ideals of its endomor- phism ring S. In this paper, we give some characterizations and properties of the structure of endomorphisms ring of M-rp-injective modules and M-lp-injective modules and the relationships between them.