Affine schemes and topological closures in the Zariski-Riemann space of valuation rings

DOI10.1016/j.jpaa.2014.07.009zbMath1320.13002arXiv1409.5113OpenAlexW2962761822MaRDI QIDQ2254331

Bruce Olberding

Publication date: 4 February 2015

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1409.5113

zbMATH Keywords

Prüfer domainaffine schemesZariski-Riemann spaceValuation rings

Mathematics Subject Classification ID

Integral closure of commutative rings and ideals (13B22) Valuations and their generalizations for commutative rings (13A18) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05) Schemes and morphisms (14A15)

Related Items (17)

A topological version of Hilbert's Nullstellensatz ⋮ The Zariski-Riemann Space of Valuation Rings ⋮ Isolated points of the Zariski space ⋮ Topological properties of semigroup primes of a commutative ring ⋮ A principal ideal theorem for compact sets of rank one valuation 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 ⋮ The Quadratic Tree of a Two-Dimensional Regular Local Ring ⋮ A connectedness theorem for spaces of valuation rings ⋮ On the topology of valuation-theoretic representations of integrally closed domains ⋮ 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 ⋮ 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 ⋮ Spectral spaces of semistar operations

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