Primeness on modules can be defined by prime elements in a suitable partially ordered
groupoid. Using a product on the lattice of submodules ℒ (M) of a module M defined in [3] …

Given a duo module M over an associative (not necessarily commutative) ring R, a Zariski
topology is defined on the spectrum Specfp (M) of fully prime R-submodules of M. We …

In this paper, we study and present a new result about retractable module. Several notions
are used to obtain more implications like category module, semi-primitive module, non …

We provide some characterizations of completely prime (completely semiprime) and 3-prime
(3-semiprime) N-groups. The relationship between a 3-prime (completely prime) N-ideal P of …

On Locally Artinian Modules 1 Introduction Page 1 International Journal of Algebra, Vol. 6, 2012,
no. 27, 1325 - 1334 On Locally Artinian Modules Adil Kadir Jabbar Department of Mathematics …

Let K be a field and E be a directed graph, called quiver in thefollowing, and let A= KE be the
path algebra that corresponds to E withcoefficients in K. An A-module M is a c-prime module …

We explore some concepts of module theory that derive from the notion of primeness, such
as first modules, and extend them to more general environments. We also provide …

In this paper we introduce the notion of equiprime N-ideals where N is a near-ring. We
consider the interconnections of equiprime, 3-prime and completely prime N-ideals of a …

The main goal of this article is to present new concept of module theory in order to study
small submodules based on the Radical of module. Depending on the relevance between …

Let R be an associative ring with nonzero identity and let M be a unitary left R− module. In
this paper, we introduce the concept of weakly primary submodules of M and give some …