hamidreza dorbidi

Let Zd(R) denotes the set of zero divisors of a ring R. Define an equivalence relation ~ on Zd(R) as follows: x ~ y if and only if ann(x) = ann(y). The graph \Gamma_E(R) is a graph associated to R whose vertices are the classes of elements in Zd(R)^* = Zd(R)\{0}, and two distinct classes [x] and [y] are joined by an edge if and only if xy = 0. In this paper we give a complete classification of finite graphs which are the compressed zero divisor graphs of reduced rings by using Goldie’s theorem.