Elementary properties of minimal and maximal points in Zariski spectra

DOI10.1016/j.jalgebra.2009.11.003zbMath1198.13023OpenAlexW2014612497MaRDI QIDQ2270118

Niels Schwartz, Marcus Tressl

Publication date: 12 March 2010

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

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2009.11.003

zbMATH Keywords

prime idealaxiomatizabilityspectral spacereduced ringGel'fand ringspseudo elementary class

Mathematics Subject Classification ID

Applications of logic to commutative algebra (13L05)

Related Items (33)

The Zariski-Riemann Space of Valuation Rings ⋮ A Zariski Topology for Modules ⋮ ON THE SUBSTITUTION THEOREM FOR RINGS OF SEMIALGEBRAIC FUNCTIONS ⋮ Locales as spectral spaces ⋮ Topological properties of semigroup primes of a commutative ring ⋮ Ultrafilter and Constructible Topologies on Spaces of Valuation Domains ⋮ A principal ideal theorem for compact sets of rank one valuation rings ⋮ Unnamed Item ⋮ Some Closure Operations in Zariski-Riemann Spaces of Valuation Domains: A Survey ⋮ On the Krull dimension of rings of continuous semialgebraic functions ⋮ Spectral reflections of topological spaces ⋮ A dual Zariski topology for modules. ⋮ Non-axiomatizability of real spectra in \(\mathcal L_{ \infty \lambda} \) ⋮ SV-rings and SV-porings ⋮ Decomposition of ideals into pseudo-irreducible ideals ⋮ Graph components of prime spectra ⋮ Sheaves and duality ⋮ On the topology of valuation-theoretic representations of integrally closed domains ⋮ Realizations of pairs and Oka families in tensor triangulated categories ⋮ Convex subrings of partially ordered rings ⋮ Affine schemes and topological closures in the Zariski-Riemann space of valuation rings ⋮ Suprema in spectral spaces and the constructible closure ⋮ Elementary properties of minimal and maximal points in Zariski spectra ⋮ Some applications of the ultrafilter topology on spaces of valuation domains, Part I ⋮ 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 ⋮ Diagonal reduction of matrices over commutative semihereditary Bezout rings ⋮ On the size of the fibers of spectral maps induced by semialgebraic embeddings ⋮ Zariski compactness of minimal spectrum and flat compactness of maximal spectrum ⋮ The constructible topology on spaces of valuation domains ⋮ On the prime spectrum of an le-module

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