A module M is called a simple-direct-injective module if, whenever A and B are simple
submodules of M with A≅ B and B is a direct summand of M, then A is a direct summand of …

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 …

The aim of this paper is to introduce the notion of nearly prime submodules as a
generalization of prime submodules. We investigate some of their basic properties and point …

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 …

We investigate prime submodules of regular modules. In particular, we shall see that every
proper submodule of a regular module M over an integral domain is prime. Although (von …

The purpose of the present paper is to prove some properties of the strongly irreducible
submodules in the arithmetical and Noetherian modules over a commutative ring. The …

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 …

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 …

In this paper, we explore the relation between small cofinite irreducibles and cyclic
submodules in the dual. As an application, we show that an Artinian module over a …

We investigate modules M having the injective property relative to nonsingular modules.
Such modules are called “N-injective modules”. It is shown that M is an N-injective R-module …