Document Type: Research Paper

Authors

1 Department of Mathematics, Islamic Azad University, Central Tehran Branch, Tehran, Iran

2 Department of Mathematics, College of Sciences, Shiraz University, Shiraz, Iran

Abstract

The annihilating-ideal graph of a commutative ring $R$ is denoted by $AG(R)$, whose vertices are all nonzero ideals of $R$ with nonzero annihilators and two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=0$. In this article, we completely characterize rings $R$ when $gr(AG(R))\neq 3$.

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