On zero divisor graph of unique product monoid rings over Noetherian reversible ring | ||
| Categories and General Algebraic Structures with Applications | ||
| مقاله 7، دوره 4، شماره 1، اردیبهشت 2016، صفحه 95-114 اصل مقاله (497.18 K) | ||
| نوع مقاله: Research Paper | ||
| نویسندگان | ||
| Ebrahim Hashemi* ؛ Abdollah Alhevaz؛ Eshag Yoonesian | ||
| Department of Mathematics, Shahrood University of Technology, Shahrood, Iran, P.O. Box: 316-3619995161. | ||
| چکیده | ||
| Let $R$ be an associative ring with identity and $Z^*(R)$ be its set of non-zero zero divisors. The zero-divisor graph of $R$, denoted by $\Gamma(R)$, is the graph whose vertices are the non-zero zero-divisors of $R$, and two distinct vertices $r$ and $s$ are adjacent if and only if $rs=0$ or $sr=0$. In this paper, we bring some results about undirected zero-divisor graph of a monoid ring over reversible right (or left) Noetherian ring $R$. We essentially classify the diameter-structure of this graph and show that $0\leq \mbox{diam}(\Gamma(R))\leq \mbox{diam}(\Gamma(R[M]))\leq 3$. Moreover, we give a characterization for the possible diam$(\Gamma(R))$ and diam$(\Gamma(R[M]))$, when $R$ is a reversible Noetherian ring and $M$ is a u.p.-monoid. Also, we study relations between the girth of $\Gamma(R)$ and that of $\Gamma(R[M])$. | ||
| کلیدواژهها | ||
| Zero-divisor graphs؛ diameter؛ Girth؛ Reversible rings؛ Polynomial rings؛ Unique product monoids؛ Monoid rings | ||
| مراجع | ||
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