Let R be a ring. We have studied rings whose projective modules have the extending
property of simple modules in [3] and [5]. In this note, we shall further study those rings when …

A ring $ R $ is regular [completely reducible] if and only if the character module of every left
$ R $-module is quasi-injective [quasiprojective]. Submodules of quasiprojective left $ R …

Artinian serial principal ideal rings and artinian serial rings are tradi-tionally called
uniserialrings and generalized uniserial rings, respectively. These rings are important …

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 …

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 …

M commutes. The first section of this paper contains results which are needed to prove a
decomposition theorem for quasi-projective modules over left perfect rings (Theorem 1.10) …

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 …

We have defined aconcept of almost M-projectives and almost M-injectives in [4] and [9],
respectively. In the first section of this paper we give some relations among lifting modules …

In [KR Fuller, on indecomposable injectives over artinian rings, Pacific J. Math. 29 (1969),
115-135, Theorem 3.1] KR Fuller gave necessary and sufficient conditions for projective left …

Note that, if X is a subset of a ring R, l (X)(resp. r (X)) is just the left (resp. right) annihilator of
X in R since(RR)*= RR. We call a ring R right PF if every faithful right R-module is a …