Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey
type: Item
instance of: scholarly article
title: Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey
zbMATH Open document ID: 1327.13016
DOI: 10.1007/978-1-4939-0925-4_9
author: Marco Fontana
author: K. Alan Loper
author: Carmelo Antonio Finocchiaro
published in: Commutative Algebra
publication date: 2015-10-07T00:00:00Z
full work available at URL: https://arxiv.org/abs/1309.5045
Mathematics Subject Classification ID: 13A18
Mathematics Subject Classification ID: 13F05
Mathematics Subject Classification ID: 13G05
zbMATH DE Number: 6490669
zbMATH Keywords: valuation domain
zbMATH Keywords: semistar operation
zbMATH Keywords: \(b\)-operation
zbMATH Keywords: e.a.b. star operation
zbMATH Keywords: spectral space
zbMATH Keywords: constructible topology
zbMATH Keywords: ultrafilter topology
zbMATH Keywords: inverse topology
zbMATH Keywords: Kronecker function ring
MaRDI profile type: Publication
OpenAlex ID: W2167253000
arXiv ID: 1309.5045
cites work: Integer-valued polynomials and Prüfer \(v\)-multiplication domains
cites work: Abstract Riemann surfaces of integral domains and spectral spaces
cites work: Kronecker function rings and abstract Riemann surfaces
cites work: On certain distinguished spectral sets
cites work: Spectral Spaces and Ultrafilters
cites work: The constructible topology on spaces of valuation domains
cites work: Ultrafilter and Constructible Topologies on Spaces of Valuation Domains
cites work: Topologically defined classes of commutative rings
cites work: A Krull-type theorem for the semistar integral closure of an integral domain
cites work: Kronecker function rings: A general approach.
cites work: Q3436764
cites work: A generalization of Kronecker function rings and Nagata rings
cites work: The Patch Topology and the Ultrafilter Topology on the Prime Spectrum of a Commutative Ring
cites work: Cancellation properties in ideal systems: A classification of e.a.b. semistar operations
cites work: Q5661989
cites work: Kronecker Function Rings and Generalized Integral Closures
cites work: Kronecker Function Rings of Transcendental Field Extensions
cites work: Prime Ideal Structure in Commutative Rings
cites work: Q4049183
cites work: Places of algebraic function fields in arbitrary characteristic
cites work: The Ordering of Spec R
cites work: Sequence domains and integer-valued polynomials
cites work: A classification of all 𝐷 such that {𝐼𝑛𝑡}(𝐷) is a Prüfer domain
cites work: Imbedding of an abstract variety in a complete variety
cites work: A generalization of the imbedding problem of an abstract variety in a complete variety
cites work: Affine schemes and topological closures in the Zariski-Riemann space of valuation rings
cites work: Q4078145
cites work: Q4093552
cites work: Jaffard-Ohm correspondence and Hochster duality
cites work: Compactification of varieties
cites work: Sheaves of abelian \(l\)-groups
cites work: Elementary properties of minimal and maximal points in Zariski spectra
cites work: Rigid analytic spaces
cites work: Relative Riemann-Zariski spaces
cites work: Prüfer algebraic spaces
cites work: The compactness of the Riemann manifold of an abstract field of algebraic functions
cites work: The reduction of the singularities of an algebraic surface
cites work: Reduction of the singularities of algebraic three dimensional varieties
description: scientific article