PERFECTNESS OF THE ANNIHILATOR GRAPH OF ARTINIAN COMMUTATIVE RINGS

‎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 and‎‎y 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.

کلیدواژه ها:

Artinian ring‎ ، ‎Annihilator graph‎ ، ‎Perfectness