PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS | ||
| Journal of Algebraic Systems | ||
| دوره 10، شماره 2، فروردین 2023، صفحه 335-343 اصل مقاله (145.47 K) | ||
| نوع مقاله: Original Manuscript | ||
| شناسه دیجیتال (DOI): 10.22044/jas.2022.11358.1571 | ||
| نویسندگان | ||
| M. Adlifard1؛ Sh. Payrovi* 2 | ||
| 1Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran. | ||
| 2Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-1-6818, Qazvin, Iran. | ||
| چکیده | ||
| Let $R$ be a commutative ring and $Z(R)$ be the set of its zero-divisors. The annihilator graph of $R$, denoted by $AG(R)$ is a simple undirected graph whose vertex set is $Z(R)^*$, the set of all nonzero zero-divisors of $R$, and two distinct vertices $x$ and $y$ are adjacent if and only if ${\rm ann}_R(xy)\neq {\rm ann}_R(x)\cup {\rm ann}_R(y)$. In this paper, perfectness of the annihilator graph for some classes of rings is investigated. More precisely, we show that if $R$ is an Artinian ring, then $AG(R)$ is perfect. | ||
| کلیدواژهها | ||
| Artinian ring؛ Annihilator graph؛ Perfectness | ||
| مراجع | ||
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