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arXiv · 0707.1525

The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring

Marco Fontana·K. Alan Loper
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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 $R$.

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Marco Fontana, K. Alan Loper. 2007-10-14. The patch topology and the ultrafilter topology on the prime spectrum of a commutative ring. https://arxiv.org/abs/0707.1525

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