The M-principal graph of a commutative ring |
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| Authors: | M J Nikmehr F Heydari |
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| Institution: | 1. Faculty of Mathematics, K.N. Toosi University of Technology, P. O. Box 16315-1618, Tehran, Iran
2. Department of Mathematics, College of Basic Sciences, Karaj Branch, Islamic Azad University, Alborz, Iran
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| Abstract: | Let \(R\) be a commutative ring and \(M\) be an \(R\) -module. In this paper, we introduce the \(M\) -principal graph of \(R\) , denoted by \(M-PG(R)\) . It is the graph whose vertex set is \(R\backslash \{0\}\) , and two distinct vertices \(x\) and \(y\) are adjacent if and only if \(xM=yM\) . In the special case that \(M=R, M-PG(R)\) is denoted by \(PG(R)\) . The basic properties and possible structures of these two graphs are studied. Also, some relations between \(PG(R)\) and \(M-PG(R)\) are established. |
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