arXiv subjects

A. Moussavi

Publications and source records attributed to A. Moussavi.

4 recordsLinked to original sources

arXiv2025

Exploring Metric and Strong Metric Dimensions in Inclusion Ideal Graphs of Commutative Rings

The inclusion ideal graph of a commutative unitary ring $R$ is the (undirected) graph $In(R)$ whose vertices all non-trivial ideals of $R$ and two distinct vertices are adjacent if and only if one of them is a proper subset of the other one. In this paper, the metric dimension of $In(R)$ is discussed. Moreover, the structure of the resolving graph of $In(R)$ is characterized and as an application, we compute the strong metric dimension of $In(R)$.

math.CO↗

arXiv2023

Strong resolving graph of the intersection graph in commutative rings

The intersection graph of ideals associated with a commutative unitary ring $R$ is the graph $G(R)$ whose vertices all non-trivial ideals of $R$ and there exists an edge between distinct vertices if and only if the intersection of them is non-zero. In this paper, the structure of the resolving graph of $G(R)$ is characterized and as an application, we evaluate the strong metric dimension of $G(R)$.

math.CO↗

arXiv2016

S-Noetherian generalized power series rings

Let R be a ring with identity, (M;\leq) a commutative positive strictly ordered monoid and w_m an automorphism for each m \in M . The skew generalized power series ring R[[M,w]] is a common generalization of (skew) polynomial rings, (skew) power series rings, (skew) Laurent polynomial rings, (skew) group rings, and Mal'cev Neumann Laurent series rings. If S\subset R is a multiplicative set, then R is called right S-Noetherian, if for each ideal I of R, Is \subseteq J\subseteq I for some s\in S and some finitely generated right ideal J . Unifying and generalizing a number of known results, we study transfers of S-Noetherian property to the ring R[[M,w]]. We also show that the ring R[[M,w]] is left Noetherian if and only if R is left Noetherian and M is finitely generated. Generalizing a result of Anderson and Dumitrescu, we show that,when S\subset R is a-anti-Archimedean multiplicative set with a an automorphism of R, then R is right S-Noetherian if and only if the skew polynomial ring R[x,a] is right S-Noetherian.

math.RA↗

arXiv2016

The ascending chain condition for principal left or right ideals of skew generalized power series rings

Let $R$ be a ring, $(S,\leq)$ a strictly ordered monoid and $ω: S\rightarrow End(R)$ a monoid homomorphism. In this paper we study the ascending chain conditions on principal left (resp. right) ideals of the skew generalized power series ring $R[[S,ω]]$. Among other results, it is shown that $R[[S,ω]]$ is a right archimedean reduced ring if $S$ is an Artinian strictly totally ordered monoid, $R$ is a right archimedean and $S$-rigid ring which satisfies the ACC on annihilators and $ω_s$ preserves nonunits of $R$ for each $s\in S$. As a consequence we deduce that the power series rings, Laurent series rings, skew power series rings, skew Laurent series rings and generalized power series rings are reduced satisfying the ascending chain condition on principal left (or right) ideals. It is also proved that, the skew Laurent polynomial ring $R[x,x^{-1};α]$ satisfies \emph{ACCPL(R)}, if $R$ is $α$-rigid and satisfies \emph{ACCPL(R)} and the $ACC$ on left(resp. right) annihilators. Examples are provided to illustrate and delimit our results.

math.RA↗