This article is a sequel to the recent three papers on “virtually semisimple modules and
rings,” by Behboodi et al., which two of them appeared in the Algebras and Representation …

Recall that a module M is called distributive if K∩(L+ N)= K∩ L+ K∩ N for any submodules
K, L, N. Clearly, submodules and quotient modules of a distributive module are distributive …

Let R be a ring and M be an R-module. In this paper we investigate modules M such that
every (simple) cosingular R-module is M-projective. We prove that every simple cosingular …

Modules in which every submodule is isomorphic to a direct summand is called virtually
semisimple. In this article, we carry out a study of virtually semisimple modules over a …

Let $ R $ be a commutative ring with identity and $ M $ be a unitary $ R $-module. A
submodule $ N $ of $ M $ is called a dense submodule if ${\rm {Hom}} _R (M/N, E_R (M)) …

A module M is said to satisfy the condition (℘∗) if M is a direct sum of a projective module
and a quasi-continuous module. By Huynh and Rizvi (J. Algebra 223 (2000) 133; …

Throughout this paper, all rings considered are integral domains, the dimension of a ring R,
denoted dimR, means its Krull dimension, and all module are unital. Let R be a ring and M …

Throughout this paper, $ R $ is an associative ring (not necessarily commutative) with
identity and $ M $ is a right $ R $-module with unitary. In this paper, we introduce a new …

Let R be a commutative ring with identity. A proper submodule N of an R-module M will be
called prime [resp. n-almost prime], if for r∈ R and a∈ M with ra∈ N [resp. ra∈ N\(N: M) n …