Scholarlink

<p>Let <i>R</i> be a commutative ring with identity. The notion of <i>S</i>-<i>J</i>-ideal was introduced in U. Tekir, S. Koc, and K. H. Oral (2017) as a generalization of <i>J</i>-ideal. We introduce a weaker version of <i>J</i>-ideals by defining the concept of weakly <i>S</i>-<i>J</i>-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>-<i>J</i>-ideal of <i>R</i> if whenever <i>ab</i> ∈ <i>I</i> for <i>a, b</i> ∈ <i>R</i>, then there exists <i>s</i> ∈ <i>S</i> such that <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(sa \in {\cal{J}}(R)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>s</mi> <mi>a</mi> <mo>∈</mo> <mrow> <mrow> <mi mathvariant="script">J</mi> </mrow> </mrow> <mo stretchy="false">(</mo> <mi>R</mi> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation> or <i>sb</i> ∈ <i>I</i>. We investigate many properties and characterizations of weakly <i>S</i>-<i>J</i>-ideals.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Weakly S-J-ideal

  • 期刊论文

  • 发表日期：

    2026年3月27日

查看全文
  • Sihem Smach

摘要

Let R be a commutative ring with identity. The notion of S-J-ideal was introduced in U. Tekir, S. Koc, and K. H. Oral (2017) as a generalization of J-ideal. We introduce a weaker version of J-ideals by defining the concept of weakly S-J-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-J-ideal of R if whenever ab ∈ I for a, b ∈ R, then there exists s ∈ S such that \(sa \in {\cal{J}}(R)\) s a ∈ J ( R ) or sb ∈ I. We investigate many properties and characterizations of weakly S-J-ideals.