arXiv subjects

Y. Azimi

Publications and source records attributed to Y. Azimi.

5 recordsLinked to original sources

arXiv2024

On the prime spectrum of the amalgamations

Let $f:R\to S$ be a ring homomorphism and $J$ be an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we will deepen the study of the prime spectrum of the amalgamations and characterize when $R\bowtie^fJ$ is a pm-ring. We also investigate the transfer of compactly packed and properly zipped property on amalgamated constructions.

math.AC↗

arXiv2024

The zero-divisor graph of an amalgamated algebra

Let $R$ and $S$ be commutative rings with identity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(r,f(r)+j)\mid r\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we generalize and improve recent results on the computation of the diameter of the zero-divisor graph of amalgamated algebras and obtain new results. In particular, we provide new characterizations for completeness of the zero-divisor graph of amalgamated algebra, as well as, a complete description for the diameter of the zero-divisor graph of amalgamations in the special case of finite rings.

math.AC↗

arXiv2024

(Generalized) filter properties of the amalgamated algebra

Let $R$ and $S$ be commutative rings with unity, $f:R\to S$ a ring homomorphism and $J$ an ideal of $S$. Then the subring $R\bowtie^fJ:=\{(a,f(a)+j)\mid a\in R$ and $j\in J\}$ of $R\times S$ is called the amalgamation of $R$ with $S$ along $J$ with respect to $f$. In this paper, we determine when $R\bowtie^fJ$ is a (generalized) filter ring.

math.AC↗

arXiv2017

Pr\"ufer conditions under the amalgamated construction

In this paper we improve the recent results on the transfer of Pr\"ufer, Gaussian and arithmetical conditions on amalgamated constructions. As an application we provide an answer to a question posed by Chhiti, Jarrar, Kabbaj and Mahdou as well as we construct various examples.

math.AC↗

arXiv2016

Cohen-Macaulay properties under the amalgamated construction

Let $A$ and $B$ be commutative rings with unity, $f:A\to B$ a ring homomorphism and $J$ an ideal of $B$. Then the subring $A\bowtie^fJ:=\{(a,f(a)+j)|a\in A$ and $j\in J\}$ of $A\times B$ is called the amalgamation of $A$ with $B$ along $J$ with respect to $f$. In this paper, we study the property of Cohen-Macaulay in the sense of ideals which was introduced by Asgharzadeh and Tousi, a general notion of the usual Cohen-Macaulay property (in the Noetherian case), on the ring $A\bowtie^fJ$. Among other things, we obtain a generalization of the well-known result that when the Nagata's idealization is Cohen-Macaulay.

math.AC↗