In this paper, we study the class of modules having the property that if any pure submodule
is isomorphic to a direct summand of such a module then the pure submodule is itself a …

Let R be a commutative ring and C a semidualizing R-module. We investigate the relations
between C-flat modules and C-FP-injective modules and use these modules and their …

Quasi-principally injective modules were studied in [12]. In this note we introduce the
concept dual to quasi-principally injective modules. It is proved that. these modules are …

In this paper, we introduce and study the dual notion of simple-direct-injective modules.
Namely, a right R-module M is called simple-direct-projective if, whenever A and B are …

A ring R is called a right C-injective ring if every homomorphism from a closed right ideal of
R to RR can be extended to one from RR to RR. It is clear that a right CS ring must be right C …

Let M be a right R-module. A right R-module N is called small principally M-injective (briefly,
SP-M-injective) if, every R-homomorphism from a small and principal submodule of M to N …

Recently, in a series of papers “simple” versions of direct-injective and direct-projective
modules have been investigated. These modules are termed as “simple-direct-injective” and …

Let R be a ring. A right R-module M is called minimal quasi-injective if every homomorphism
from a simple submodule of M to M can be extended to an endomorphism of M. Some …

Mathematical Journal of Okayama University Page 1 Mathematical Journal of Okayama
University Volume 51, Issue 1 2009 Article 6 A NOTE ON ALMOST INJECTIVE MODULES …

In this work, the notion of pseudo-injectivity relative to a class of submodules (namely, ic-
pseudo-injectivity) has been introduced and studied, which is a proper generalization of …