The constructible topology on spaces of valuation domains

DOI10.1090/S0002-9947-2013-05741-8zbMath1297.13007arXiv1206.3521MaRDI QIDQ2855925

Marco Fontana, K. Alan Loper, Carmelo Antonio Finocchiaro

Publication date: 23 October 2013

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1206.3521

zbMATH Keywords

Zariski topologyspectral spaceconstructible topologyultrafilter topologyKronecker function ring

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

Radical semistar operations, Topological properties of localizations, flat overrings and sublocalizations, The strong ultrafilter topology on spaces of ideals, The Zariski-Riemann Space of Valuation Rings, Isolated points of the Zariski space, Towards a classification of stable semistar operations on a Prüfer domain, Topological properties of semigroup primes of a commutative ring, Alexandroff topology of algebras over an integral domain, A principal ideal theorem for compact sets of rank one valuation rings, Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey, Open Problems in Commutative Ring Theory, Some topological considerations on semistar operations, The tree of quadratic transforms of a regular local ring of dimension two, The sets of star and semistar operations on semilocal Prüfer domains, An ultrapower analogue of the Kronecker function ring, On the topology of valuation-theoretic representations of integrally closed domains, Affine schemes and topological closures in the Zariski-Riemann space of valuation rings, Suprema in spectral spaces and the constructible closure, The ideal theory of intersections of prime divisors dominating a normal Noetherian local domain of dimension two, The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications, Topology, intersections and flat modules, New Distinguished Classes of Spectral Spaces: A Survey, Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings, When the Zariski space is a Noetherian space, Topological properties of subsets of the Zariski space, The space of homogeneous preserving semistar operations on graded domains, Spectral spaces of semistar operations

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Cancellation properties in ideal systems: A classification of e.a.b. semistar operations
• Kronecker function rings and abstract Riemann surfaces
• Abstract Riemann surfaces of integral domains and spectral spaces
• Topologically defined classes of commutative rings
• Géométrie analytique rigide et applications. (Ridgid analytic geometry and applications)
• Places of algebraic function fields in arbitrary characteristic
• Integer-valued polynomials and Prüfer \(v\)-multiplication domains
• Elementary properties of minimal and maximal points in Zariski spectra
• Irredundant intersections of valuation overrings of two-dimensional noetherian domains
• Overrings of two-dimensional noetherian domains representable by noetherian spaces of valuation rings
• Rigid analytic spaces
• Compactification of varieties
• The reduction of the singularities of an algebraic surface
• Kronecker Function Rings of Transcendental Field Extensions
• The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring
• Kronecker Function Rings and Generalized Integral Closures
• Ultrafilter and Constructible Topologies on Spaces of Valuation Domains
• Prime Ideal Structure in Commutative Rings
• The compactness of the Riemann manifold of an abstract field of algebraic functions