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

Carmelo Antonio Finocchiaro; Marco Fontana

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

Carmelo Antonio Finocchiaro, Marco Fontana (2010)

Actes des rencontres du CIRM

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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 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...