Topological properties of localizations, flat overrings and sublocalizations
Dario Spirito
TL;DR
This paper investigates the topological structure of localizations, flat overrings, and sublocalizations of integral domains, revealing their spectral space properties and conditions for proconstructibility within the space of all overrings.
Contribution
It provides a topological characterization of localizations and related overrings, including conditions for proconstructibility, extending the understanding of their spectral space structure.
Findings
The set of localizations forms a spectral space.
Conditions identified for localizations to be proconstructible.
Topological properties of quotient rings, flat overrings, and sublocalizations analyzed.
Abstract
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructible subspace of the space of all overrings. We then study the same problems in the case of quotient rings, flat overrings and sublocalizations.
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