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The Co-annihilating-ideal Graphs of Commutative Rings

Published online by Cambridge University Press:  20 November 2018

Saeeid Akbari ,
Abbas Alilou ,
Jafar Amjadi  and
Seyed Mahmoud Sheikholeslami
Saeeid Akbari
Affiliation:
Department of Mathematical Sciences, Sharif University of Technology, Tehran, I. R. Iran e-mail: s_akbari@sharif.edu e-mail: a-alilou@azaruniv.edu
Abbas Alilou
Affiliation:
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran e-mail: j-amjadi@azaruniv.edu e-mail: s.m.sheikholeslami@azaruniv.edu
Jafar Amjadi
Affiliation:
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran e-mail: j-amjadi@azaruniv.edu e-mail: s.m.sheikholeslami@azaruniv.edu
Seyed Mahmoud Sheikholeslami
Affiliation:
Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran e-mail: j-amjadi@azaruniv.edu e-mail: s.m.sheikholeslami@azaruniv.edu
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Abstract

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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 $\text{Ann}\left( I \right)\,\cap \,\text{Ann}\left( J \right)\,=\,\left\{ 0 \right\}$. In this paper we initiate the study of the co-annihilating ideal graph of a commutative ring and we investigate its properties.

Keywords

13A1516N40commutative ringco-annihilating-ideal graph
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 60 , Issue 1 , 01 March 2017 , pp. 3 - 11
Copyright
Copyright © Canadian Mathematical Society 2017

References

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