Search engine for discovering works of Art, research articles, and books related to Art and Culture
ShareThis
Javascript must be enabled to continue!

On 2-absorbing quasi primary submodules

View through CrossRef
Let R be a commutative ring with nonzero identity, and let M be a nonzero unital R-module. In this article, we introduce the concept of 2-absorbing quasi primary submodules which is a generalization of prime submodules. We define 2-absorbing quasi primary submodule as a proper submodule N of M having the property that abm ? N, then ab ? ?(N :R M) or am ? radM(N) or bm ? radM(N): Various results and examples concerning 2-absorbing quasi primary submodules are given.
Title: On 2-absorbing quasi primary submodules
Description:
Let R be a commutative ring with nonzero identity, and let M be a nonzero unital R-module.
In this article, we introduce the concept of 2-absorbing quasi primary submodules which is a generalization of prime submodules.
We define 2-absorbing quasi primary submodule as a proper submodule N of M having the property that abm ? N, then ab ? ?(N :R M) or am ? radM(N) or bm ? radM(N): Various results and examples concerning 2-absorbing quasi primary submodules are given.

Related Results

Semi-Coessential and Semi-Coclosed Submodules
Semi-Coessential and Semi-Coclosed Submodules
In this paper, we study and introduce two new concepts in module theory: semi-coessential submodules and semi-coclosed submodules. These notions are generalizations of the classica...
WE-primary submodules and WE-quasi-prime submodules
WE-primary submodules and WE-quasi-prime submodules
In this paper we introduced and study  two concepts one of is a subclass of a class of weakly primary submodules called WE-primary submodules and the other of a subclass of weakly ...
WES-2-Absorbing Submodules and WEQ-2-Absorbing Submodules
WES-2-Absorbing Submodules and WEQ-2-Absorbing Submodules
In this research, we introduced and studied, the concepts of WES-2-absorbing submodules and WEQ-2-absorbing submodules as a stronger form of the concepts of weakly semi-2-absorbing...
Extend Nearly Pseudo Quasi-2-Absorbing Submodules (II)
Extend Nearly Pseudo Quasi-2-Absorbing Submodules (II)
The concept of the Extend Nearly Pseudo Quasi-2-Absorbing submodules was recently introduced by Omar A. Abdullah and Haibat K. Mohammadali in 2022, where he studies thi...
Minimal Prime and Semiprime Submodules
Minimal Prime and Semiprime Submodules
Prime and semiprime submodules are important generalizations of prime and semiprime ideals to module theory over commutative rings. However, minimal or smallest prime/semiprime sub...
Pseudo Primary-2-Absorbing Submodules and Some Related Concepts
Pseudo Primary-2-Absorbing Submodules and Some Related Concepts
      Let  be a commutative ring with identity. The aim of this paper is introduce the notion of a pseudo primary-2-absorbing submodule as generalization of 2-absorbing submodule a...
Approximaitly Semi-Prime Submodules and Some Related Concepts
Approximaitly Semi-Prime Submodules and Some Related Concepts
    We introduce in this paper the concept of approximaitly semi-prime submodules of unitary left -module  over a commutative ring  with identity as a generalization of a prime sub...
On Nearly Prime Submodules of Unitary Modules
On Nearly Prime Submodules of Unitary Modules
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 out the...

Back to Top