On the Diameter of Zero-Divisor Graphs of Idealizations with Respect to Integral Domain

Abstract

Let R be a ring with unity and let M be an R - module. Let R(+)M be the idealization of the ring R by the R - module M. In this paper, we give new results on the diameter of Γ(R(+)M) when R is an integral domain.

Key words and phrases. Zero - divisor graphs, Idealization rings.

2000 Mathematics Subject Classification. Primary: 13A99, Secondary: 13A15