The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring

Abstract

Abstract Let R be a commutative ring and let Spec(R) denote the collection of prime ideals of R. We define a topology on Spec(R) by using ultrafilters and demonstrate that this topology is identical to the well-known patch or constructible topology. The proof is accomplished by use of a von Neumann regular ring canonically associated with R. Key Words: Constructible topologyPatch topologyPrime spectrumUltrafiltervon Neumann regular ringZariski topology2000 Mathematics Subject Classification: 13A1513A1713B1014A05 Notes Communicated by I. Swanson.

Locations

• arXiv (Cornell University) - View - PDF
• Applied General Topology (Universitat Politècnica de València) - View - PDF
• Communications in Algebra - View