A Zariski-like topology on the ideal spectrum of a ring

Abstract

The purpose of this paper is to introduce a Zariski-like topology on the spectrum of all proper ideals of a ring. We show that the space is T_0, quasi-compact, and every irreducible closed subset has a unique generic point. Furthermore, this space is weaker than a spectral space and if the ring has a non-trivial idempotent element then the space has a closed disconnected subspace.

arXiv commentThis paper no longer valid with respect to some results. Also, the new paper "Ideal spaces: An extension of structure spaces of rings" submitted covers some of the work in this paper. But the new paper is not a replacement of this paper