In the present survey paper, we present several new classes of Hochster’s spectral spaces “occurring in nature,” actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The general setting is the space of the semistar operations (of finite type), endowed with a Zariski-like topology, which turns out to be a natural topological extension of the space of the overrings of an integral domain, endowed with a topology introduced by Zariski. One of the key tool is a recent characterization of spectral spaces, based on the ultrafilter topology, given in Finocchiaro, Commun Algebra, 42:1496-1508, 2014, [15]. Several applications are also discussed.

New distinguished classes of spectral spaces: A survey

FINOCCHIARO, CARMELO ANTONIO;
2016-01-01

Abstract

In the present survey paper, we present several new classes of Hochster’s spectral spaces “occurring in nature,” actually in multiplicative ideal theory, and not linked to or realized in an explicit way by prime spectra of rings. The general setting is the space of the semistar operations (of finite type), endowed with a Zariski-like topology, which turns out to be a natural topological extension of the space of the overrings of an integral domain, endowed with a topology introduced by Zariski. One of the key tool is a recent characterization of spectral spaces, based on the ultrafilter topology, given in Finocchiaro, Commun Algebra, 42:1496-1508, 2014, [15]. Several applications are also discussed.
2016
978-3-319-38853-3
978-3-319-38855-7
Constructible; Gabriel-Popescu localizing system; Inverse and ultrafilter topologies; Kronecker function ring; Riemann-Zariski space of valuation domains; Spectral space and spectral map; Star and semistar operations; Zariski
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.11769/377561
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