Czechoslovak Mathematical Journal

Czechoslovak Mathematical Journal, first online, pp. 1-14

Weakly $S$-2-absorbing ideals

Smach Sihem

Received September 23, 2024. Published online January 26, 2025.

Abstract: Let $R$ be a commutative ring with identity. The notion of $S$-2-absorbing ideal was introduced by G. Ulucak, Ü. Tekir, S. Koç (2020) as a generalization of 2-absorbing ideal. We introduce $a$ weaker version of 2-absorbing ideals by defining the concept of weakly-$S$-2-absorbing ideal. Let $S\subseteq R$ be a multiplicatively closed subset of $R$. A proper ideal $I$ of $R$ disjoint with $S$ is called a weakly $S$-2-absorbing ideal of $R$ if whenever $abc\in I$ for $a,b,c\in R$ then there exists $s\in S$ such that $sab\in I$ or $sbc\in I$ or $sac\in I$. We investigate many properties and characterizations of weakly $S$-2-absorbing ideals.

Keywords: $S$-2-absorbing ideal; weakly $S$-2-absorbing ideal; $S$-prime ideal

Classification MSC: 13A15, 13A99

DOI: 10.21136/CMJ.2025.0397-24

PDF available at: Institute of Mathematics CAS

References:
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Affiliations: Smach Sihem, Department of Mathematics, Faculty of Sciences, Avenue of the Environment, 5019 Monastir, Tunisia, e-mail: smach_sihem@yahoo.com

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