2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/139872Let 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 $R$.A Remark was added at the end of the paper. To appear in Comm. AlgebraCommutative AlgebraAlgebraic Geometry13A99; 14A05; 13L05The patch topology and the ultrafilter topology on the prime spectrum of a commutative ringtext