arXiv subjects

Moutu Abdou Salam Moutui

Publications and source records attributed to Moutu Abdou Salam Moutui.

5 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↗

arXiv2018

Gaussian and Prüfer conditions in bi-amalgamated algebras

Let $f: A\rightarrow B$ and $g: A\rightarrow C$ be two ring homomorphisms and let $J$ (resp., $J'$) be an ideal of $B$ (resp., $C$) such that $f^{-1}(J)=g^{-1}(J')$. In this paper, we investigate the transfer of the notions of Gaussian and Prüfer properties to the bi-amalgamation of $A$ with $(B,C)$ along $(J,J')$ with respect to $(f,g)$ (denoted by $A\bowtie^{f,g}(J,J')),$ introduced and studied by Kabbaj, Louartiti and Tamekkante in 2013. Our results recover well known results on amalgamations in \cite{Finno} and generate new original examples of rings satisfying these properties.

math.AC↗

arXiv2014

Prûfer property in amalgamated algebras along an ideal

Let $f : A \rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani's and Yassemi's work (see \cite{y}). Also, we investigate the transfer of Prüfer domain concept to commutative rings with zero divisors in the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009 (see \cite{AFF1} and \cite{AFF2}). Our aim is to provide new classes of commutative rings satisfying this property.

math.AC↗

arXiv2014

Self injective property in amalgamated algebra along an ideal

Let $f: A\rightarrow B$ be a ring homomorphism and let $J$ be an ideal of $B$. In this paper, we investigate the transfer of self-injective property to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009. We give also a characterization of $A\bowtie^fJ$ to be quasi-Frobenius.

math.AC↗

arXiv2014

Gaussian property in amalgamated algebras along an ideal

Let $f : A \rightarrow B$ be a ring homomorphism and $J$ be an ideal of $B$. In this paper, we investigate the transfer of Gaussian property to the amalgamation of $A$ with $B$ along $J$ with respect to $f$ (denoted by $A\bowtie^fJ),$ introduced and studied by D'Anna, Finocchiaro and Fontana in 2009.

math.AC↗