When the Zariski space is a Noetherian space

DOI10.1215/00192082-7773701zbMath1420.13049arXiv1807.08645OpenAlexW2883740005MaRDI QIDQ2315249

Dario Spirito

Publication date: 2 August 2019

Published in: Illinois Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1807.08645

zbMATH Keywords

valuation domainoverringNoetherian spaceZarisky topology

Mathematics Subject Classification ID

Valuations and their generalizations for commutative rings (13A18) Ideals and multiplicative ideal theory in commutative rings (13A15) Valuation rings (13F30)

Related Items (2)

Isolated points of the Zariski space ⋮ Topological properties of subsets of the Zariski space

Cites Work

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• Factoring ideals in integral domains
• Kronecker function rings and abstract Riemann surfaces
• Abstract Riemann surfaces of integral domains and spectral spaces
• On Jaffard domains
• Topologically defined classes of commutative rings
• Pseudo-valuation domains
• Jaffard families and localizations of star operations
• Affine schemes and topological closures in the Zariski-Riemann space of valuation rings
• Non-compact subsets of the Zariski space of an integral domain
• Compactification of varieties
• Topology, intersections and flat modules
• Topological Aspects of Irredundant Intersections of Ideals and Valuation Rings
• The constructible topology on spaces of valuation domains
• Noetherian Spaces of Integrally Closed Rings with an Application to Intersections of Valuation Rings
• Principal ideal theorems for holomorphy rings in fields.
• Prime Ideal Structure in Commutative Rings
• The compactness of the Riemann manifold of an abstract field of algebraic functions

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