Ultrafilter and Constructible Topologies on Spaces of Valuation Domains

DOI10.1080/00927872.2011.651760zbMath1310.13006arXiv1202.2451OpenAlexW2150533300MaRDI QIDQ5326259

K. Alan Loper, Marco Fontana, Carmelo Antonio Finocchiaro

Publication date: 5 August 2013

Published in: Communications in Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1202.2451

zbMATH Keywords

valuation domainultrafilterconstructible topologyprime spectrumZarisky topology

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Integral domains (13G05) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (10)

On some spectral spaces associated to tensor triangulated categories ⋮ The Zariski-Riemann Space of Valuation Rings ⋮ Some topology on zero-dimensional subrings of product of rings ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ The tree of quadratic transforms of a regular local ring of dimension two ⋮ Spectral Spaces and Ultrafilters ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part II ⋮ New Distinguished Classes of Spectral Spaces: A Survey ⋮ Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings ⋮ The constructible topology on spaces of valuation domains

Cites Work

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• The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring
• A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
• TOTAL VALUATION RINGS OFK(X, σ) CONTAININGK
• The compactness of the Riemann manifold of an abstract field of algebraic functions

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