The Co-annihilating-ideal Graphs of Commutative Rings

Canadian mathematical bulletin

Seyed Mahmoud Sheikholeslami¹  Jafar Amjadi¹  Saeeid Akbari²  Abbas Alilou¹ 

[1] Department of Mathematics, Azarbaijan Shahid Madani University, Tabriz, I.R. Iran;Department of Mathematical Sciences, Sharif University of Technology, Tehran, I. R. Iran

关键词: commutative ring;    co-annihilating ideal graph;   

DOI  :  10.4153/CMB-2016-017-1

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

Let $R$ be a commutative ring with identity. Theco-annihilating-ideal graph of $R$, denoted by $mathcal{A}_R$,isa graph whose vertex set is the set of all non-zero proper idealsof $R$ and two distinct vertices $I$ and $J$ are adjacentwhenever ${operatorname {Ann}}(I)cap {operatorname {Ann}}(J)={0}$. In this paper weinitiate the study of the co-annihilating ideal graph of acommutative ring and we investigate its properties.

【 授权许可】

Unknown