Spectral spaces and ultrafilters

2013/09/20 by Carmelo Antonio Finocchiaro, Carmelo A. Finocchiaro, Finocchiaro, Carmelo A. · 1 citation
Mathematics · #13A99 #14A05 #54D80 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #FOS: Mathematics #Rings, Modules, and Algebras #math.AC #msc:13A99 #msc:14A05 #msc:54D80

paper · pdf · doi:10.48550/arxiv.1309.5190

16 pages. To appear in Communications in Algebra

arxiv created 2013/09/20 · openalex publication_date 2013/09/20 · arxiv updated 2013/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let X be the prime spectrum of a ring. In [arXiv:0707.1525] the authors define a topology on X by using ultrafilters and they show that this topology is precisely the constructible topology. In this paper we generalize the construction given in [arXiv:0707.1525] and, starting from a set X and a collection of subsets F of X, we define by using ultrafilters a topology on X in which \mathcal F is a collection of clopen sets. We use this construction for giving a new characterization of spectral spaces and several new examples of spectral spaces.

Citations

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

Cited by

• Closure operators on semilattice-ordered semigroups and spectrality of induced operations

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