We introduce and study a nontrivial generalization of uniserial modules and rings. A module
is called weakly uniserial if its submodules are comparable regarding embedding. Also, a …

For a right module M, we prove that M is simple-injective if and only if M is min-N-injective for
every cyclic right module N. The rings whose simple-injective right modules are injective are …

An R− module M is called almost uniserial if any two non-isomorphic submodules of M are
comparable. A ring R is an almost left uniserial ring if RR is almost uniserial. In this paper …

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 …

We study the class of virtually uniserial modules and rings as a nontrivial generalization of
uniserial modules and rings. An R-module M is virtually uniserial if for every finitely …

A theorem due to Warfield states that “a ring R is left serial if and only if every (finitely
generated) projective left R-module is serial” and a theorem due to Tuganbaev states that “a …

A torsion-free module is called quasi-regular if each cyclic submodule is a quasi-summand.
This article characterizes torsion-free Abelian groups that are quasi-regular as modules over …

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 …

In this paper we study almost uniserial rings and modules. An R− module M is called almost
uniserial if any two nonisomorphic submodules are linearly ordered by inclusion. A ring R is …

We introduce the notion of almost pseudo-injective modules (AP-injective modules), which
generalizes the idea of pseudo-injective and almost injective modules. In support, we …