Let K be a field, and let A be a subring of K. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar(K pipe A) of all valuation domains having K as quotient field and containing A. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar(K pipe A). We extend results regarding distinguished spectral topologies on spaces of valuation domains. © 2013 Copyright Taylor and Francis Group, LLC.

Finocchiaro C, Fontana M, & Loper A. (2013). Ultrafilter and constructible topologies on spaces of valuation domains. COMMUNICATIONS IN ALGEBRA, 41(5), 1825-1835 [10.1080/00927872.2011.651760].

Ultrafilter and constructible topologies on spaces of valuation domains

FINOCCHIARO, CARMELO ANTONIO;;
2013

Abstract

Let K be a field, and let A be a subring of K. We consider properties and applications of a compact, Hausdorff topology called the "ultrafilter topology" defined on the space Zar(K pipe A) of all valuation domains having K as quotient field and containing A. We show that the ultrafilter topology coincides with the constructible topology on the abstract Riemann-Zariski surface Zar(K pipe A). We extend results regarding distinguished spectral topologies on spaces of valuation domains. © 2013 Copyright Taylor and Francis Group, LLC.
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/11590/134794
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