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# The Co-annihilating-ideal Graphs of Commutative Rings

Published:2016-11-15
Printed: Mar 2017
• Saeeid Akbari,
Department of Mathematical Sciences, Sharif University of Technology, Tehran, I. R. Iran
• Abbas Alilou,
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
• Seyed Mahmoud Sheikholeslami,
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran
 Format: LaTeX MathJax PDF

## Abstract

Let $R$ be a commutative ring with identity. The co-annihilating-ideal graph of $R$, denoted by $\mathcal{A}_R$, is a graph whose vertex set is the set of all non-zero proper ideals of $R$ and two distinct vertices $I$ and $J$ are adjacent whenever ${\operatorname {Ann}}(I)\cap {\operatorname {Ann}}(J)=\{0\}$. In this paper we initiate the study of the co-annihilating ideal graph of a commutative ring and we investigate its properties.
 Keywords: commutative ring, co-annihilating ideal graph
 MSC Classifications: 13A15 - Ideals; multiplicative ideal theory 16N40 - Nil and nilpotent radicals, sets, ideals, rings

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