The strong ultrafilter topology on spaces of ideals
| Autor: | Carmelo Antonio Finocchiaro, K. Alan Loper |
|---|---|
| Rok vydání: | 2016 |
| Předmět: |
Zariski topology
Algebra and Number Theory Commutative ring Spectral topology Spectrum of a ring 010102 general mathematics Mathematics::General Topology Extension topology 010103 numerical & computational mathematics Topology 01 natural sciences Comparison of topologies Mathematics::Logic Subbase Compact-open topology Product topology General topology 0101 mathematics Mathematics |
| Zdroj: | Journal of Algebra. 461:226-243 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2016.04.023 |
| Popis: | The patch/constructible refinement of the Zariski topology on the prime spectrum of a commutative ring is well known and well studied. Recently, Fontana and Loper gave an equivalent definition of this topology using ultrafilters. In this note we distinguish between two different types of ultrafilter convergence and use them to define two new topologies on the prime spectrum of a ring. We study various properties of these topologies. As applications we use the ultrafilters to classify all the compact subsets of a spectral space in the Zariski topology and we classify Grothendieck's retrocompact spaces again using ultrafilters. |
| Databáze: | OpenAIRE |
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