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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
  • Jafar Amjadi,
    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
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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 commutative ring, co-annihilating ideal graph
MSC Classifications: 13A15, 16N40 show english descriptions Ideals; multiplicative ideal theory
Nil and nilpotent radicals, sets, ideals, rings
13A15 - Ideals; multiplicative ideal theory
16N40 - Nil and nilpotent radicals, sets, ideals, rings
 

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