A note on graphical representation of rings
type: Item
instance of: scholarly article
title: A note on graphical representation of rings
zbMATH Open document ID: 0838.05051
author: Pramod K. Sharma
author: S. M. Bhatwadekar
published in: Journal of Algebra
publication date: 1996-05-30T00:00:00Z
review text: Main result: Let \(R\) be a commutative ring with identity. \(R\) may be regarded as a graph with elements of \(R\) as vertices. Two distinct vertices \(x\) and \(y\) are said to be adjacent if and only if \(Rx+ Ry= R\). Then the chromatic number \(\chi(R)< \infty\) if and only if \(R\) is a finite ring. In this case \(\chi(R)=\text{clique } R= t+ \ell\), where \(t\) and \(\ell\) respectively denote the number of maximal ideals of \(R\) and the number of units of \(R\).
Mathematics Subject Classification ID: 05C15
Mathematics Subject Classification ID: 13A99
zbMATH DE Number: 802372
zbMATH Keywords: clique
zbMATH Keywords: commutative ring
zbMATH Keywords: chromatic number
zbMATH Keywords: number of maximal ideals
reviewed by: K. Chandrasekhara Rao
MaRDI profile type: Publication
full work available at URL: jabr.1995.1236
OpenAlex ID: W2010159669
DOI: 10.1006/JABR.1995.1236
description: scientific article; zbMATH DE number 802372