Javascript must be enabled to continue!

W-Closed Submodule and Related Concepts

Let R be a commutative ring with identity, and M be a left untial module. In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L. Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied. Furthermore, modules with chain condition on w-closed submodules are studied.

College of Education for Pure Sciences Ibn Al-Haitham

Haibat K. Mohammad Ali Mohammad E. Dahsh

Ibn AL-Haitham Journal For Pure and Applied Sciences

2018

Title: W-Closed Submodule and Related Concepts

Description:

Let R be a commutative ring with identity, and M be a left untial module.

In this paper we introduce and study the concept w-closed submodules, that is stronger form of the concept of closed submodules, where asubmodule K of a module M is called w-closed in M, "if it has no proper weak essential extension in M", that is if there exists a submodule L of M with K is weak essential submodule of L then K=L.

Some basic properties, examples of w-closed submodules are investigated, and some relationships between w-closed submodules and other related modules are studied.

Furthermore, modules with chain condition on w-closed submodules are studied.

Back

In this work we discuss the concept of pure-maximal denoted by (Pr-maximal) submodules as a generalization to the type of R- maximal submodule, where a proper submodule of a...

Closed-coessential and Closed-coclosed Submodules

The aim of this study is to present the concept of closed-coessential submodule and closed-coclosed submodule, the consideration of certain properties. Allow R be a ring with ident...

Pseudo Quasi-2-Absorbing Submodules and Some Related Concepts

Let R be a ring and let A be a unitary left R-module. A proper submodule H of an R-module A is called 2-absorbing , if rsaâˆˆH, where r,sâˆˆR,aâˆˆA, implies that either raâˆˆH or s...

W-visible submodules and W-fully visible modules

In this paper, we presented a special type of submodule named W-visible submodule, which is weaker than the visible submodule, where a proper submodule W of a T-module X is said to...

gw-S-prime submodules

Let R be a ring with identity and S ⊆ R be a multiplicative closed subset. Let M be an R-module. Sevim et al. [15] introduced the concept of S-prime submodule. A submodule P of M w...

Nearly Primary-2-Absorbing Submodules and other Related Concepts

Our aim in this paper is to introduce the notation of nearly primary-2-absorbing submodule as generalization of 2-absorbing submodule where a proper submodule of an -module is ca...

On h-purifiable submodule of QTAG-module

Different concepts and decomposition theorems have been done for QTAG-modules by a number of authors. The concept of quasi $h$-pure submodules were introduced and different charact...

Z-Small Submodules and Z-Hollow Modules

A submodule Ϝ of an R-module Ε is called small in Ε if whenever , for some submodule W of Ε , implies . In this paper , we introduce the notion of Ζ-small submodule , where a pro...

Email:
Password:

Email:

W-Closed Submodule and Related Concepts

Related Results