arXiv subjects

Mohamed Chhiti

Publications and source records attributed to Mohamed Chhiti.

4 recordsLinked to original sources

arXiv2024

When every finitely generated ideal is S-principal

In this paper, we introduce the concept of $S$-Bézout ring, as a generalization of Bézout ring. We investigate the relationships between $S$-Bézout and other related classes of rings. We establish some characterizations of $S$-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 $S$-Bézout rings subject to various ring theoretical properties. Furthermore, we introduce the notion of nonnil $S$-Bézout ring and establish some characterizations.

math.AC↗

arXiv2010

Prüfer- like conditions in the amalgamated duplication of a ring along an ideal

In this paper, we consider five possible extensions of the Prüfer domain notion to the case of commutative rings with zero-divisors. We investigate the transfer of these Prüfer-like properties between a ring $R$ and $R\bowtie I$; his amalgamated duplication along some ideal $I$, and then generate new and original families of rings with these properties.

math.AC↗

arXiv2009

Homological dimensions of the amalgamated duplication of a ring along a pure ideal

The aim of this paper is to study the classical global and weak dimensions of the amalgamated duplication of a ring $R$ along a pure ideal $I$.

math.AC↗

arXiv2009

Some homological properties of an amalgamated duplication of a ring along an ideal

In this work, we investigate the transfer of some homological properties from a ring $R$ to his amalgamated duplication along some ideal $I$ of $R$, and then generate new and original families of rings with these properties.

math.AC↗