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 …

Let 𝑅 be a commutative ring with identity, and let 𝑀 be a unital 𝑅-module. A submodule 𝑁 of
𝑀 is called a dense submodule, if 𝑀=∑ 𝜑𝜑 (𝑁) where 𝜑 runs over all the 𝑅-morphisms from …

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 …

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 left module $ M $ over an arbitrary ring is called an $\mathcal {RD} $-module (or an
$\mathcal {RS} $-module) if every submodule $ N $ of $ M $ with ${\rm Rad}(M)\subseteq N …

Let $ R $ be a commutative ring with identity and let $ M $ be an $ R $-module. A proper
submodule $ P $ of $ M $ is called strongly prime submodule if $(P+ Rx: M) y P $ for $ x, y M …

In this paper, we study some more properties on direct-injective modules in the context of
endoregular, SSP and SIP modules. We find the equivalent condition for a directinjective …

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 …

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 …

In this paper, all rings are commutative with nonzero identity. Let $ M $ be an $ R $-module.
A proper submodule $ N $ of $ M $ is called a classical prime submodule, if for each $ m\in …