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

Journal of Linear and Topological Algebra

مقاله 5، دوره 04، شماره 03، آبان 2015، صفحه 209-216   

نوع مقاله: Research Paper

نویسندگان

M. Ahrari^{* 1}؛ Sh. A. Safari Sabet¹؛ B. Amini²

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

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

چکیده

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 $gr(AG(R))\neq 3$.

کلیدواژه‌ها

annihilating-ideal graph؛ star graph؛ bipartite graph؛ girth

مراجع

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