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

Aisuriya Sudprasert; Hoang Dinh Hai; Supunnee Sanpinij

Aisuriya Sudprasert
Hoang Dinh Hai
Supunnee Sanpinij

Keywords: M-p-injective modules, quasi-p-injective modules, right quasi-p-injective modules, self-generators, quasi weakly-p-injective, quasi-rp-injective, quasi-lp-injective.

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 investigated the class of M-rp-injective modules and M-lp-injective modules, and proved that for a ﬁnitely generated Kasch module M, ifM 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 endomorphism 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