It is well known that the concept of left serial ring is a Morita invariant property and a theorem
due to Nakayama and Skornyakov states that “for a ring R, all left R-modules are serial if and …

A theorem due to Nakayama and Skornyakov states that “a ring R is an Artinian serial ring if
and only if all left R-modules are serial” and a theorem due to Warfield state that “a …

The present paper is a sequel to our previous work on almost uniserial rings and modules,
which appeared in the Journal of Algebra in 2016; it studies rings over which every (left and …

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 …

An $ R $-module $ M $ is called virtually uniserial if for every finitely generated submodule
$0\neq K\subseteq M $, $ K/$ Rad $(K) $ is virtually simple. In this paper, we generalize …

Let R be an associative ring and M a unitary left R-module. An R-module M is said to be
uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum …

A right R-module M is called uniserial if its submodules are linearly ordered by inclusion, ie,
for any submodules A and B of M, either A⊆ B or B⊆ A. A ring R is right uniserial if it is …

Let R be an associative ring and M a unitary left R-module. An R-module M is said to be
uniserial if its submodules are linearly ordered by inclusion. A serial module is a direct sum …

We define prime uniserial modules as a generalization of uniserial modules. We say that an
R-module M is prime uniserial (℘-uniserial) if its prime submodules are linearly ordered by …

A serial ring (generalized uniserial in the terminology of Nakayama) is one whose left and
right free modules are direct sums of modules with unique finite composition series …