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

Finocchiaro, Carmelo Antonio; Fontana, Marco

doi:10.5802/acirm.45

Finocchiaro, Carmelo Antonio ¹ ; Fontana, Marco ²

¹ C.A.F. - Dipartimento di Matematica Università degli studi Roma Tre Largo San Leonardo Murialdo 1, 00146 Roma, Italy
² M.F. - Dipartimento di Matematica Università degli studi Roma Tre Largo San Leonardo Murialdo 1, 00146 Roma, Italy

Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 111-114.

Résumé

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 $Zar (K | A)$ , introduced in the previous Part I. After recalling that $Zar (K | A)$ is a spectral space, we give an explicit description of $Zar (K | A)$ 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.

Publié le : 2011-10-20

Zbl

DOI : 10.5802/acirm.45

Mots clés : Valuation domain, (semi)star operation, prime spectrum, Zariski topology, constructible topology, filter and ultrafilter, Prüfer domain.

Affiliations des auteurs :

Finocchiaro, Carmelo Antonio ¹ ; Fontana, Marco ²

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Finocchiaro, Carmelo Antonio; Fontana, Marco. Some applications of the ultrafilter topology on spaces of valuation domains, Part II. Actes des rencontres du CIRM, Tome 2 (2010) no. 2, pp. 111-114. doi : 10.5802/acirm.45. http://www.numdam.org/articles/10.5802/acirm.45/

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