Some applications of the ultrafilter topology on spaces of valuation domains, Part II

Finocchiaro, Carmelo Antonio, and Fontana, Marco. "Some applications of the ultrafilter topology on spaces of valuation domains, Part II." Actes des rencontres du CIRM 2.2 (2010): 111-114. <http://eudml.org/doc/196293>.

@article{Finocchiaro2010,
abstract = {Let $K$ be a field and $A$ be a subring of $K$. In the present note, we present the main applications of the so called ultrafilter topology on the space $\{\rm Zar\}(K|A)$, introduced in the previous Part I. After recalling that $\{\rm Zar\}(K|A)$ is a spectral space, we give an explicit description of $\{\rm Zar\}(K|A)$ as the prime spectrum of a ring (even in the case when the quotient field of $A$ is a proper subfield of $K$). Moreover, we provide applications of the topological material previously introduced to the study of representations of integrally closed domains and valuative semistar operations.},
affiliation = {C.A.F. - Dipartimento di Matematica Università degli studi Roma Tre Largo San Leonardo Murialdo 1, 00146 Roma, Italy; M.F. - Dipartimento di Matematica Università degli studi Roma Tre Largo San Leonardo Murialdo 1, 00146 Roma, Italy},
author = {Finocchiaro, Carmelo Antonio, Fontana, Marco},
journal = {Actes des rencontres du CIRM},
keywords = {Valuation domain; (semi)star operation; prime spectrum; Zariski topology; constructible topology; filter and ultrafilter; Prüfer domain},
language = {eng},
number = {2},
pages = {111-114},
publisher = {CIRM},
title = {Some applications of the ultrafilter topology on spaces of valuation domains, Part II},
url = {http://eudml.org/doc/196293},
volume = {2},
year = {2010},
}

TY - JOUR
AU - Finocchiaro, Carmelo Antonio
AU - Fontana, Marco
TI - Some applications of the ultrafilter topology on spaces of valuation domains, Part II
JO - Actes des rencontres du CIRM
PY - 2010
PB - CIRM
VL - 2
IS - 2
SP - 111
EP - 114
AB - Let $K$ be a field and $A$ be a subring of $K$. In the present note, we present the main applications of the so called ultrafilter topology on the space ${\rm Zar}(K|A)$, introduced in the previous Part I. After recalling that ${\rm Zar}(K|A)$ is a spectral space, we give an explicit description of ${\rm Zar}(K|A)$ as the prime spectrum of a ring (even in the case when the quotient field of $A$ is a proper subfield of $K$). Moreover, we provide applications of the topological material previously introduced to the study of representations of integrally closed domains and valuative semistar operations.
LA - eng
KW - Valuation domain; (semi)star operation; prime spectrum; Zariski topology; constructible topology; filter and ultrafilter; Prüfer domain
UR - http://eudml.org/doc/196293
ER -