Published online by Cambridge University Press: 20 November 2018
The purpose of this paper is to continue the work of [7]. Throughout the paper all notations shall have the same meanings as those in [7]; that is, the ring R is commutative with identity, B(R) is the set of idempotents in R, Spec B(R) is the set of prime ideals in B(R), and Ue for e in B(R) denotes the set {x/x in Spec B(R) with 1—e in x}. Then from [6] we know that {Ue/e in B(R)} forms a basic open set for a topology imposed in Spec B(R) and this topological space is totally disconnected, compact and Hausdorff.