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

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Weakly S-2-absorbing ideals

  • 期刊论文

  • 发表日期：

    2025年1月26日

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  • Smach Sihem

摘要

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 ⊆ 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 ∈ I for a, b, c ∈ R then there exists s ∈ S such that sab ∈ I or sbc ∈ I or sac ∈ I. We investigate many properties and characterizations of weakly S-2-absorbing ideals.