Flat topology on the spectra of quantales
| Autor: | George Georgescu |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
0209 industrial biotechnology
Zariski topology Pure mathematics Mathematics::Commutative Algebra Logic Quantale Flat topology 02 engineering and technology Commutative ring Congruence relation Prime (order theory) 020901 industrial engineering & automation Artificial Intelligence 0202 electrical engineering electronic engineering information engineering 020201 artificial intelligence & image processing Commutative property Minimal prime Mathematics |
| Zdroj: | Fuzzy Sets and Systems. 406:22-41 |
| ISSN: | 0165-0114 |
| DOI: | 10.1016/j.fss.2020.08.009 |
| Popis: | Several topologies can be defined on the prime, the maximal and the minimal prime spectra of a commutative ring; among them, we mention the Zariski topology, the patch topology and the flat topology. By using these topologies, Tarizadeh and Aghajani obtained recently new characterizations of various classes of rings: Gelfand rings, clean rings, absolutely flat rings, mp - rings, etc. The aim of this paper is to generalize some of their results to quantales, structures that constitute a good abstractization for lattices of ideals, filters and congruences. We shall study the flat and the patch topologies on the prime, the maximal and the minimal prime spectra of a coherent quantale. By using these two topologies one obtains new characterization theorems for hyperarchimedean quantales, normal quantales, B-normal quantales, mp - quantales and PF - quantales. The general results can be applied to several concrete algebras: commutative rings, bounded distributive lattices, MV-algebras, BL-algebras, residuated lattices, commutative unital l - groups, etc. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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