Ahrari, M., Safari Sabet, S., Amini, B. (2015). On the girth of the annihilating-ideal graph of a commutative ring. Journal of Linear and Topological Algebra (JLTA), 04(03), 209-216.

M. Ahrari; Sh. A. Safari Sabet; B. Amini. "On the girth of the annihilating-ideal graph of a commutative ring". Journal of Linear and Topological Algebra (JLTA), 04, 03, 2015, 209-216.

Ahrari, M., Safari Sabet, S., Amini, B. (2015). 'On the girth of the annihilating-ideal graph of a commutative ring', Journal of Linear and Topological Algebra (JLTA), 04(03), pp. 209-216.

Ahrari, M., Safari Sabet, S., Amini, B. On the girth of the annihilating-ideal graph of a commutative ring. Journal of Linear and Topological Algebra (JLTA), 2015; 04(03): 209-216.

On the girth of the annihilating-ideal graph of a commutative ring

^{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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