16 citations · 35 across the 24 of their papers we have counts for
7 papers · 1 filter
The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences
Giulio Peruginelli, Dario Spirito
Let be a valuation domain with quotient field . Given a pseudo-convergent sequence in , we study two constructions associating to a valuation domain of lyi…
When the Zariski space is a Noetherian space
Dario Spirito
We characterize when the Zariski space (where is an integral domain, is a field containing and is integrally closed in ) and the set $\mathrm…
Decomposition and classification of length functions
Dario Spirito
We study decompositions of length functions on integral domains as sums of length functions constructed from overrings. We find a standard representation when the integral domain a…
The upper Vietoris topology on the space of inverse-closed subsets of a spectral space and applications
Carmelo A. Finocchiaro, Marco Fontana, Dario Spirito
Given an arbitrary spectral space , we consider the set of all nonempty subsets of that are closed with respect to the inverse topology. We i…
Star operations on Kunz domains
Dario Spirito
We study star operations on Kunz domains, a class of analytically irreducible, residually rational domains associated to pseudo-symmetric numerical semigroups, and we use them to r…
Topological properties of localizations, flat overrings and sublocalizations
Dario Spirito
We study the set of localizations of an integral domain from a topological point of view, showing that it is always a spectral space and characterizing when it is a proconstructibl…
Calculating the density of solutions of equations related to the Pólya-Ostrowski group through Markov chains
Dario Spirito
Motivated by a problem in the theory of integer-valued polynomials, we investigate the natural density of the solutions of equations of the form $θ_uu_q(n)+θ_ww_q(n)+θ_2\frac{n(n+1…