New Distinguished Classes of Spectral Spaces: A Survey

DOI10.1007/978-3-319-38855-7_5zbMath1353.13004arXiv1510.04443OpenAlexW2963615540MaRDI QIDQ2826740

Dario Spirito, Marco Fontana, Carmelo Antonio Finocchiaro

Publication date: 18 October 2016

Published in: Springer Proceedings in Mathematics & Statistics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1510.04443

zbMATH Keywords

Kronecker function ringGabriel-Popescu localizing systemRiemann-Zariski space of valuation domainsspectral space and spectral mapstar and semistar operationsZariski, constructible, inverse and ultrafilter topologies

Mathematics Subject Classification ID

Morphisms of commutative rings (13B10) Integral domains (13G05) Ideals and multiplicative ideal theory in commutative rings (13A15) Relevant commutative algebra (14A05) Injective and flat modules and ideals in commutative rings (13C11) Chain conditions, finiteness conditions in commutative ring theory (13E99)

Related Items

Topological properties of localizations, flat overrings and sublocalizations, A topological version of Hilbert's Nullstellensatz, The Zariski-Riemann Space of Valuation Rings, Topological properties of semigroup primes of a commutative ring, Closure operations, continuous valuations on monoids and spectral spaces, The tree of quadratic transforms of a regular local ring of dimension two, Integral domains with finitely many spectral semistar operations, Proper spaces are spectral, A connectedness theorem for spaces of valuation rings, Unnamed Item, Jaffard families and localizations of star operations, Suprema in spectral spaces and the constructible closure, The Zariski topology on sets of semistar operations without finite-type assumptions, Topology, intersections and flat modules, Abstractly constructed prime spectra

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