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 P of M with (P :R M) ∩ S = ∅ is said to be an S-2-absorbing submodule if there exists an element s ∈ S and whenever abm ∈ P for some a, b ∈ R and m ∈ M, then sab ∈ (P :R M) or sam ∈ P or sbm ∈ P. Many examples, characterizations and properties of S-2-absorbing submodules are given. Moreover, we use them to characterize von Neumann regular modules in the sense [9].

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On weakly 2-absorbing primary submodules of modules over commutative rings

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

In this paper, we introduce the concept of graded weakly 2-absorbing primary submodules as a generalization of graded weakly 2-absorbing primary ideals. A number of results concerning these classes of graded submodules and their homogeneous components are given.

On Graded Weakly 2-Absorbing Primary Submodules

On $n-$absorbing primary submodules

Let R be a commutative ring with identity and let M be a unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is a multiplicatively closed subset of R. A submodule P of M with (P:R M)∩S=∅ is said to be a weakly S-2-absorbing submodule if there exists an element s ∈ S such that whenever a,b∈R and m∈M with 0≠abm∈P, then sab∈(P: M) or sam∈P or sbm∈P. We give the characterizations, properties and examples of weakly S-2-absorbing submodules.

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On weakly 2-absorbing primary submodules of modules over commutative rings

Citations

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

On Graded Weakly 2-Absorbing Primary Submodules

On $n-$absorbing primary submodules

On Weakly S-2-Absorbing Submodules

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