The \(M\)-principal graph of a commutative ring
type: Item
instance of: scholarly article
title: The \(M\)-principal graph of a commutative ring
zbMATH Open document ID: 1340.05125
author: F. Heydari
author: M. J. Nikmehr
published in: Periodica Mathematica Hungarica
publication date: 2014-08-14T00:00:00Z
full work available at URL: https://arxiv.org/abs/1305.6192
review text: In the present paper, the authors introduce the \(M\)-principal graph of \(R\), denoted by \(M - \mathrm{PG}(R)\), where \(M\) is an \(R\)-module of a commutative ring \(R\). It is the graph whose vertex set is \(R\setminus\{0\}\), and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(x M = y M\). They study properties of \(\mathrm{PG}(R)\) and some relations between \(\mathrm{PG}(R)\), when \(R=M\), and \(M - \mathrm{PG}(R)\) are established. In particular, the authors consider the graph \(\mathrm{PG}(\mathbb{Z}_n)\) for each positive integer \(n > 1\).
reviewed by: Vilmar Trevisan
Mathematics Subject Classification ID: 05C25
Mathematics Subject Classification ID: 05C69
Mathematics Subject Classification ID: 13A99
Mathematics Subject Classification ID: 13C99
zbMATH DE Number: 6330550
zbMATH Keywords: \(M\)-principal graph
zbMATH Keywords: commutative ring
zbMATH Keywords: module
zbMATH Keywords: clique number
zbMATH Keywords: independence number
Wikidata QID: Q59322053
MaRDI profile type: Publication
OpenAlex ID: W2142614293
arXiv ID: 1305.6192
cites work: On the coloring of the annihilating-ideal graph of a commutative ring
cites work: Minimal prime ideals and cycles in annihilating-ideal graphs
cites work: The Classification of the Annihilating-Ideal Graphs of Commutative Rings
cites work: The total graph and regular graph of a commutative ring
cites work: Q4520250
cites work: Q4101884
cites work: Q5563439
cites work: Q3739243
cites work: The unit graph of a left Artinian ring
cites work: The regular digraph of ideals of a commutative ring
DOI: 10.1007/S10998-014-0029-0
description: scientific article; zbMATH DE number 6330550