In this paper, we study rings with the property that every cyclic module is almost-injective
(CAI). It is shown that R is an Artinian serial ring with J (R)^ 2= 0 J (R) 2= 0 if and only if R is …

In this paper certain injectivity conditions in terms of extensions of monomorphisms are
considered. In particular, it is proved that a ring R is a quasi-Frobenius ring if and only if …

Let R be a ring and M a left R-module. An R-module N is called a cofinite extension of M in
case and is finitely generated. We say that M has the property CE (resp. CEE) if M has a …

In this paper, we generalize the concept of direct-injective modules to fi nite-direct-injective
modules. Various basic properties of these modules are studied. We show that the class of fi …

The notion of a U-module was introduced and thoroughly investigated in as a strict and
simultaneous generalization of quasi-continuous, square-free and automorphism-invariant …

Rings for which every singular left module is injective, called SI-rings, were introduced and
studied by Goodearl [4]. He characterized such rings as those nonsingular ones for which …

Let I be an ideal of a ring R. Consider the following conditions on R: 1. If X is a finitely
generated submodule of a finitely generated projective module P, then X= A⨁ B where is a …

We shall introduce the notion of uniformly classical primary submodule that generalizes the
concept of uniformly primary ideal as given by JA Cox and AJ Hetzel. We also advance the …

A class C of modules over a unitary ring is said to be socle fine if whenever M, N∊ C with
Soc (M)≅ Soc (N) then M≅ N. In this work we characterize certain types of rings by requiring …