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.A., 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;FONTANA, Marco;
2013-01-01
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
