Suprema in spectral spaces and the constructible closure
| Autor: | CARMELO ANTONIO FINOCCHIARO, Spirito, D. |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Spectral spaces
constructible topology specialization order overrings semistar operations General Topology (math.GN) FOS: Mathematics Commutative Algebra (math.AC) Mathematics - Commutative Algebra Constructible topology Overrings Semistar operations Specialization order Mathematics - General Topology |
| Zdroj: | Università degli Studi di Catania-IRIS |
| Popis: | Given an arbitrary spectral space $X$, we endow it with its specialization order $\leq$ and we study the interplay between suprema of subsets of $(X,\leq)$ and the constructible topology. More precisely, we investigate about when the supremum of a set $Y\subseteq X$ exists and belongs to the constructible closure of $Y$. We apply such results to algebraic lattices of sets and to closure operations on them, proving density properties of some distinguished spaces of rings and ideals. Furthermore, we provide topological characterizations of some class of domains in terms of topological properties of their ideals. |
| Databáze: | OpenAIRE |
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