no. 2
Some applications of the ultrafilter topology on spaces of valuation domains, Part II
Finocchiaro, Carmelo Antonio1 ; Fontana, Marco2
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, Troisième Rencontre Internationale sur les Polynômes à Valeurs Entières, Tome 2 (2010) no. 2, pp. 111-114

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 :
DOI : 10.5802/acirm.45
Keywords: Valuation domain, (semi)star operation, prime spectrum, Zariski topology, constructible topology, filter and ultrafilter, Prüfer domain.

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 
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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, Troisième Rencontre Internationale sur les Polynômes à Valeurs Entières, Tome 2 (2010) no. 2, pp. 111-114. doi: 10.5802/acirm.45

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