An ideal-based zero-divisor graph of 2-primal near-rings

Abstract

In this paper, we give topological properties of collection of prime ideals in 2-primal near-rings. We show that Spec(N), the spectrum of prime ideals, is a compact space, and Max(N), the maximal ideals of N, forms a compact T1-subspace. We also study the zero-divisor graph ΓI(R) with respect to the completely semiprime ideal I of N. We show that ΓP(R), where P is a prime radical of N, is a connected graph with diameter less than or equal to 3. We characterize all cycles in the graph ΓP(R). © 2009 The Korean Mathematical Society.