A module M over a ring is called simple-direct-injective if, whenever A and B are simple
submodules of M with A≅ B and B⊆⊕ M, we have A⊆⊕ M. Various basic properties of …

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 …

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 …

We prove that for a ring $ R $, the following are equivalent:(i) Every right $ R $-module is a
direct sum of extending modules, and (ii) $ R $ has finite type and right colocal type (ie …

Rings Whose Modules Are {oplus}-Supplemented Page 1 Ž . Journal of Algebra 218, 470487
1999 Article ID jabr.1998.7830, available online at http:rrwww.idealibrary.com on Rings Whose …

The concept of weak relative-injectivity of modules was introduced originally in [10], where it
is shown that a semiperfect ring R is such that every cyclic right module is embeddable …

A ring R is called a V-ring, respectively SSI-ring, respectively QII-ring if simple, respectively
semisimple, respectively quasi-injective, right R-modules are injective. We show that R is …

Theorem (K6the-Cohen-Kaplansky). A commutative ring R has the property that each of its R-
modules is a direct sum of cyclic modules if and only if R is an artinian principal ideal ring …

R is called a right WV-ring if each simple right R-module is injective relative to proper cyclics.
If R is a right WV-ring, then R is right uniform or a right V-ring. It is shown that a right WV-ring …

6 0 GOEL AND JAIN self-injective ring (or if R is a semiperfect ring) then each cyclic R-
module is a-injective if and only if R is a direct sum of semisimple artinian ring and a finite …