Some Relations That Concerning Localization of Certain Types of Submodules (original) (raw)

Localization and Some Properties of Certain Types of Modules

Evaluation Study of Three Diagnostic Methods for Helicobacter pylori Infection, 2017

In this paper Artinian and locally prime modules are studied and some characterizations of locally prime modules are given. Some conditions are given under which locally prime modules are almost prime modules and a nonzero module is a locally prime module. Some properties of Artinian and locally Artinian modules are given. Also, strongly reduced modules, primally reduced modules, radically reduced modules and some other types are studied and investigated and some properties of these types of modules are proved. In addition, some relations that concerning these types of modules are established and some characterizations of them are given.

Some results concerning localization of commutative rings and modules

International Journal of Algebra, 2015

In this paper some results that concerning localization of commutative rings and modules are proved. It also, studies the effect of localization on certain types of ideals and modules such as G−ideals, G−submodules, G−weakly submodules and G−modules. Several conditions are given under which certain properties of such types of algebraic structures are preserved under localization.

On locally multiplication modules

International Mathematical Forum, 2016

The main aim of this paper is to study locally multiplication modules and to extend some properties of multiplication modules to locally multiplication modules. Some conditions are obtained under which locally multiplication modules satisfy ascending and descending chain conditions on certain types of submodules. Also, those locally multiplication modules which are finitely generated are classified. In addition to the above, some conditions are given each of which makes a proper submodule of an R−module as a prime submodule.

Pure submodules of multiplication modules

Contributions to Algebra and Geometry, 2004

Abstract: The purpose of this paper is to investigate pure submodules of multiplication modules. We introduce the concept of idempotent submodule generalizing idempotent ideal. We show that a submodule of a multiplication module with pure annihilator is pure if and ...

Some Properties of Multiplication Modules

Journal of the Indonesian Mathematical Society, 2017

Let M be an R-module. The module M is called multiplication if for anysubmodule N of M we have N = IM, where I is an ideal of R. In this paperwe state some basic properties of multiplication modules.

On Modules over Local Rings

Analele Universitatii "Ovidius" Constanta - Seria Matematica, 2016

This paper is dealed with a special local ring A and modules over A. Some properties of modules, that are constructed over the real plural algebra, are investigated. Moreover a module is constructed over the linear algebra of matrix M

2-Maximal Submodules and Related Concepts

Journal of University of Anbar for Pure Science

"Throughout this paper R represents commutative ring with identity and M is unitary left R-module", the purpose of this paper is to study new concept (up to our knowledge) , named 2maximal submodule which is a generalization of maximal submodule , "where a submodule N of an Rmodule M is called 2-maximal" submodul of M if and only if is 2-regular R-module. Many characterizations and properties of 2-maximal submodules are given. Moreover we studied the behavior of 2-maximal submodule in some classes of module. Finally we give the sufficient condition 2-maximal submodules to be semi-maximal weak-maximal submodules are introduced .

Multiplication Modules

Communications in Algebra, 2001

Let R be a commutative ring with identity and M be a unital R-module. Then M is called a multiplication module provided for every submodule N of M there exists an ideal I of R such that N = IM. Our objective is to investigate properties of prime and semiprime submodules of multiplication modules.

Some remarks on primal submodules

2008

In this paper, we study the primal submodules of a module over a commutative ring with non-zero identity. We generalize the primal decomposition of ideals (see [2]) to that of submodules. Let R be a commutative ring, M an R-module and N a submodule of M. We establish a decomposition of N as an intersection of primal submodules of M. We show that if R is a Prüfer domain of finite character, then N has a primal decomposition. Also we prove that the representation of submodules as reduced intersections of primal submodules is unique.