Given an arbitrary spectral space X, we endow it with its specialization order <= and we study the interplay between suprema of subsets of (X, <=) and the constructible topology. More precisely, we examine when the supremum of a set Y subset of 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.
Suprema in spectral spaces and the constructible closure
Spirito, D
2020-01-01
Abstract
Given an arbitrary spectral space X, we endow it with its specialization order <= and we study the interplay between suprema of subsets of (X, <=) and the constructible topology. More precisely, we examine when the supremum of a set Y subset of 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.File in questo prodotto:
File | Dimensione | Formato | |
---|---|---|---|
Suprema in spectral spaces and the constructible closure.pdf
non disponibili
Tipologia:
Versione Editoriale (PDF)
Licenza:
Non pubblico
Dimensione
433.48 kB
Formato
Adobe PDF
|
433.48 kB | Adobe PDF | Visualizza/Apri Richiedi una copia |
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.