Scholarlink

<p>In this paper, we introduce a ring in which every finitely generated regular ideal is <i>S</i>-principal (where <i>S</i> is a mulptiplicative set) and we call it a regular <i>S</i>-Bézout ring, as a generalization of <i>S</i>-Bézout ring. We establish some characterizations of regular <i>S</i>-Bézout rings. We study this property in various contexts of commutative rings including direct product, localization, trivial ring extensions and amalgamation rings. Our results allow us to construct new original classes of regular <i>S</i>-Bézout rings subject to various ring theoretical properties.</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

When every finitely generated regular ideal is S-principal

  • 期刊论文

  • 发表日期：

    2025年9月1日

查看全文
  • Mohamed Chhiti,
  • Salah Eddine Mahdou

摘要

In this paper, we introduce a ring in which every finitely generated regular ideal is S-principal (where S is a mulptiplicative set) and we call it a regular S-Bézout ring, as a generalization of S-Bézout ring. We establish some characterizations of regular S-Bézout rings. We study this property in various contexts of commutative rings including direct product, localization, trivial ring extensions and amalgamation rings. Our results allow us to construct new original classes of regular S-Bézout rings subject to various ring theoretical properties.