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.
Fontana, M., LOPER K., A. (2008). The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring. COMMUNICATIONS IN ALGEBRA, 36, 2917-2922 [10.1080/00927870802110326].