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