In memory of my father. Let X be the prime spectrum of a ring. In Fontana and Loper [5] the authors define a topology on X by using ultrafilters and show that this topology is precisely the constructible topology. In this paper we generalize the construction given in Fontana and Loper [5] and, starting from a set X and a collection of subsets ℱ of X, we define by using ultrafilters a topology on X in which ℱ is a collection of clopen sets. We use this construction for giving a new characterization of spectral spaces and several examples of spectral spaces. © 2014 Copyright Taylor and Francis Group, LLC.

Spectral Spaces and Ultrafilters

Finocchiaro C. A.
2014

Abstract

In memory of my father. Let X be the prime spectrum of a ring. In Fontana and Loper [5] the authors define a topology on X by using ultrafilters and show that this topology is precisely the constructible topology. In this paper we generalize the construction given in Fontana and Loper [5] and, starting from a set X and a collection of subsets ℱ of X, we define by using ultrafilters a topology on X in which ℱ is a collection of clopen sets. We use this construction for giving a new characterization of spectral spaces and several examples of spectral spaces. © 2014 Copyright Taylor and Francis Group, LLC.
Constructible topology; Spectral space; Ultrafilter; Zariski topology
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/383254
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 19
  • ???jsp.display-item.citation.isi??? 18
social impact