PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS
نویسندگان
1 Department of Mathematics, Roudbar Branch, Islamic Azad University, Roudbar, Iran.
2 Department of Mathematics, Imam Khomeini International University, P.O. Box 34149-1-6818, Qazvin, Iran.
doi
10.22044/jas.2022.11358.1571چکیده
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 vertexset 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.
