ON THE ANNIHILATOR GRAPH OF GROUP RINGS

Let R be a commutative ring with nonzero identity and G be a nontrivial finite group. Also, let Z(R) be the set of zero-divisors of R and, for a epsilon Z(R), let ann(a) = {r epsilon R | ra = 0}. The annihilator graph of the group ring RG is defined as the graph AG(RG), whose vertex set consists of the set of nonzero zero-divisors, and two distinct vertices x and y are adjacent if and only if ann(xy) not equal ann(x) boolean OR ann(y). In this paper, we study the annihilator graph associated to a group ring RG.