The q.Zariski topology on the quasi-primary spectrum of a ring

Abstract

Let R be a commutative ring with identity. We topologize q.Spec(R), the quasi-primary spectrum of R, in a way similar to that of defining the Zariski topology on the prime spectrum of R, and investigate the properties of this topological space. Rings whose q.Zariski topology is respectively T0, T1, irreducible or Noetherian are studied, and several characterizations of such rings are given.