Publications de l'Institut Mathématique, Nouvelle Série Vol. 97(111), pp. 225–231 (2015) 

DOMINATION NUMBER IN THE ANNIHILATINGIDEAL GRAPHS OF COMMUTATIVE RINGSReza Nikandish, Hamid Reza Maimani, Sima KianiDepartment of Mathematics, JundiShapur University of Technology, Dezful, Iran; Mathematics Section, Department of Basic Sciences, Shahid Rajaee Teacher Training University, Tehran, Iran; School of Mathematics, Institute for Research in Fundamental Sciences (IPM), Tehran, Iran; Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, IranAbstract: Let $R$ be a commutative ring with identity and $\mathbb{A}(R)$ be the set of ideals with nonzero annihilator. The annihilatingideal graph of $R$ is defined as the graph $\mathbb{AG}(R)$ with the vertex set $\mathbb{A}(R)^{*}=\mathbb{A}(R)\smallsetminus\{0\}$ and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this paper, we study the domination number of $\mathbb{AG}(R)$ and some connections between the domination numbers of annihilatingideal graphs and zerodivisor graphs are given. Keywords: annihilatingideal graph; zerodivisor graph; domination number; minimal prime ideal Classification (MSC2000): 13A15; 05C75 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.
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