<abstract xmlns="http://www.w3.org/1999/xhtml">Let <italic>R</italic> be a commutative ring and <italic>M</italic> an <italic>R</italic>-module. In this article, we introduce the concept of <italic>S</italic>-2-absorbing submodule. Suppose that <italic>S</italic> ⊆ <italic>R</italic> is a multiplicatively closed subset of <italic>R.</italic> A submodule <italic>P</italic> of <italic>M</italic> with (<italic>P</italic> :<italic>R M</italic>) ∩ <italic>S</italic> = ∅ is said to be an <italic>S</italic>-2-absorbing submodule if there exists an element <italic>s</italic> ∈ <italic>S</italic> and whenever <italic>abm</italic> ∈ <italic>P</italic> for some <italic>a, b</italic> ∈ <italic>R</italic> and <italic>m</italic> ∈ <italic>M</italic>, then <italic>sab</italic> ∈ (<italic>P</italic> :<italic>R M</italic>) or <italic>sam</italic> ∈ <italic>P</italic> or <italic>sbm</italic> ∈ <italic>P.</italic> Many examples, characterizations and properties of <italic>S</italic>-2-absorbing submodules are given. Moreover, we use them to characterize von Neumann regular modules in the sense [9].</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].

On <italic>S</italic>-2-absorbing submodules and vn-regular modules

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

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On -2-absorbing submodules and vn-regular modules

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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...

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

Published Online: Sep 22, 2020

Page range: 239 - 257

Received: Aug 31, 2019

Accepted: Dec 17, 2019

DOI: https://doi.org/10.2478/auom-2020-0030

Keywords
2-absorbing submodule, -2-absorbing submodule, von Neumann regular module

© 2020 Gülşen Ulucak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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

Published Online: Sep 22, 2020

Page range: 239 - 257

Received: Aug 31, 2019

Accepted: Dec 17, 2019

DOI: https://doi.org/10.2478/auom-2020-0030

Keywords2-absorbing submodule, -2-absorbing submodule, von Neumann regular module

© 2020 Gülşen Ulucak et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
2-absorbing submodule, -2-absorbing submodule, von Neumann regular module