<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>Let <italic>R</italic> be a commutative ring with non-zero identity and <italic>M</italic> be a unitary <italic>R</italic>-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule <italic>N</italic> of <italic>M</italic> is said to be a 1-absorbing primary submodule if whenever non-unit elements <italic>a, b</italic> ∈ <italic>R</italic> and <italic>m</italic> ∈ <italic>M</italic> with <italic>abm</italic> ∈ <italic>N</italic>, then either <italic>ab</italic> ∈ (<italic>N</italic> :<italic><sub>R</sub>M</italic>) or <italic>m</italic> ∈ <italic>M</italic> − <italic>rad</italic>(<italic>N</italic>). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved.</p>
</abstract>

Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals to 1-absorbing primary submodules. A proper submodule N of M is said to be a 1-absorbing primary submodule if whenever non-unit elements a, b ∈ R and m ∈ M with abm ∈ N, then either ab ∈ (N :RM) or m ∈ M − rad(N). Various properties and chacterizations of this class of submodules are considered. Moreover, 1-absorbing primary avoidance theorem is proved.

1-absorbing primary submodules

Department of Electrical Electronics Engineering, Faculty of Engineering

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"1-absorbing primary submodules"}

Let R be a commutative ring with non-zero identity and M be a unitary R-module. The goal of this paper is to extend the concept of 1-absorbing primary ideals...

1-absorbing primary submodules

Published Online: Nov 23, 2021

Page range: 285 - 296

Received: Jan 03, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0045

Keywords
1-absorbing primary submodule, 1-absorbing primary ideal, 2-absorbing primary submodule

© 2021 Ece Yetkin Celikel, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

1-absorbing primary submodules

Published Online: Nov 23, 2021

Page range: 285 - 296

Received: Jan 03, 2021

Accepted: Apr 28, 2021

DOI: https://doi.org/10.2478/auom-2021-0045

Keywords1-absorbing primary submodule, 1-absorbing primary ideal, 2-absorbing primary submodule

© 2021 Ece Yetkin Celikel, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Keywords
1-absorbing primary submodule, 1-absorbing primary ideal, 2-absorbing primary submodule