# On 2-Absorbing Primary Submodules of Modules over Commutative Rings

@article{Mostafanasab2015On2P, title={On 2-Absorbing Primary Submodules of Modules over Commutative Rings}, author={Hojjat Mostafanasab and Ece Yetkin and {\"U}nsal Tekir and Ahmad Yousefian Darani}, journal={Analele Universitatii "Ovidius" Constanta - Seria Matematica}, year={2015}, volume={24}, pages={335 - 351} }

Abstract All rings are commutative with 1 ≠ 0, and all modules are unital. The purpose of this paper is to investigate the concept of 2-absorbing primary submodules generalizing 2-absorbing primary ideals of rings. Let M be an R-module. A proper submodule N of an R-module M is called a 2-absorbing primary submodule of M if whenever a; b ∈ R and m ∈ M and abm ∈ N, then am ∈ M-rad(N) or bm ∈ M-rad(N) or ab ∈(N :R M). It is shown that a proper submodule N of M is a 2-absorbing primary submodule if…

## 21 Citations

Classical 2-absorbing Submodules of Modules Over Commutative Rings

- Mathematics
- 2015

In this article, all rings are commutative with nonzero identity. Let M be an R-module. A proper submodule N of M is called a classical prime submodule, if for each m\in M and elements a,b\in R,…

On classical n-absorbing submodules

- MathematicsArabian Journal of Mathematics
- 2019

Let R a commutative ring with identity and M be a unitary R-module. In this paper, we investigate some properties of n-absorbing submodules of M as a generalization of 2-absorbing submodules. We also…

On S-2-absorbing submodules and vn-regular modules

- Mathematics
- 2020

Abstract Let R be a commutative ring and M an R-module. In this article, we introduce the concept of S-2-absorbing submodule. Suppose that S ⊆ R is a multiplicatively closed subset of R. A submodule…

On weakly S-prime submodules

- Mathematics
- 2021

Let R be a commutative ring with a non-zero identity, S be a multiplicatively closed subset of R and M be a unital R-module. In this paper, we define a submodule N of M with (N :R M) ∩ S = φ to be…

On 2-Absorbing Quasi Primary Submodules

- Mathematics
- 2017

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…

n-Absorbing Ideals of Commutative Rings and Recent Progress on Three Conjectures: A Survey

- Mathematics
- 2017

Let R be a commutative ring with 1 ≠ 0. Recall that a proper ideal I of R is called a 2-absorbing ideal of R if a, b, c ∈ R and abc ∈ I, then ab ∈ I or ac ∈ I or bc ∈ I. A more general concept than…

On S-2-absorbing primary submodules

- Filomat
- 2021

This article introduces the concept of S-2-absorbing primary submodule as a
generalization of 2-absorbing primary submodule. Let S be a multiplicatively
closed subset of a ring R and M an R-module.…

On n-Absorbing Ideals and Two Generalizations of Semiprime Ideals

- Mathematics
- 2017

Let R be a commutative ring and n be a positive integer. A proper ideal I of R is called an n-absorbing ideal if whenever x_1...x_{n+1}\in I for x_1,...,x_{n+1}\in R, then there are n of the x_i's…

On Weakly 2-Absorbing Semi-Primary Submodules of Modules over Commutative Rings

- Mathematics
- 2018

Let $R$ be a commutative ring with identity and let $M$ be a unitary $R$-module. We say that a proper submodule $N$ of $M$ is a weakly $2$-absorbing semi-primary submodule if $a_{1}, a_{2}\in R, m\in…

2-irreducible and strongly 2-irreducible ideals of commutative rings

- Mathematics
- 2015

An ideal I of a commutative ring R is said to be irreducible if it cannot be written as the intersection of two larger ideals. A proper ideal I of a ring R is said to be strongly irreducible if for…

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