Noetherian Spaces of Integrally Closed Rings with an Application to Intersections of Valuation Rings

DOI10.1080/00927870903114979zbMath1203.13027OpenAlexW2147437321MaRDI QIDQ3057721

Bruce Olberding

Publication date: 17 November 2010

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

Full work available at URL: https://doi.org/10.1080/00927870903114979

zbMATH Keywords

valuation ringsZariski topologyintegrally closed ringnoetherian spaces

Mathematics Subject Classification ID

Integral domains (13G05) Valuation rings (13F30) Dedekind, Prüfer, Krull and Mori rings and their generalizations (13F05)

Related Items (17)

Topological properties of localizations, flat overrings and sublocalizations ⋮ The Zariski-Riemann Space of Valuation Rings ⋮ Isolated points of the Zariski space ⋮ Topological properties of semigroup primes of a commutative ring ⋮ Some topological considerations on semistar operations ⋮ The tree of quadratic transforms of a regular local ring of dimension two ⋮ Integral domains having a unique Kronecker function ring ⋮ Irredundant intersections of valuation overrings of two-dimensional noetherian domains ⋮ Spectral Spaces and Ultrafilters ⋮ Overrings of two-dimensional noetherian domains representable by noetherian spaces of valuation rings ⋮ 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 ⋮ The space of homogeneous preserving semistar operations on graded domains ⋮ Spectral spaces of semistar operations

Cites Work

• On Prüfer rings
• Kronecker function rings and abstract Riemann surfaces
• The radical trace property
• Irredundant intersections of valuation overrings of two-dimensional noetherian domains
• Overrings of two-dimensional noetherian domains representable by noetherian spaces of valuation rings
• Overrings of Prüfer domains
• Overrings of Prüfer domains. II
• Irredundant intersections of valuation rings
• Minimal Prime Ideals in Commutative Semigroups
• Commutative ideal theory without finiteness conditions: Primal ideals
• Integral domains of finite character.
• Defining Families for Integral Domains of Real Finite Character
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