16 citations · 35 across the 24 of their papers we have counts for
36 papers
The local Picard group of a ring extension
Dario Spirito
Given an integral domain and a -algebra , we introduce the local Picard group as the quotient between the Picard group and the cano…
Boundness in almost Dedekind domains
Dario Spirito
We study different form of boundness for ideals of almost Dedekind domains, generalizing the notions of critical ideals, radical factorization, and SP-domains. We show that every a…
The Golomb topology of polynomial rings, II
Dario Spirito
We study the interplay of the Golomb topology and the algebraic structure in polynomial rings over a field . In particular, we focus on infinite fields of positive ch…
Distinguished classes of ideal spaces and their topological properties
Carmelo A. Finocchiaro, Amartya Goswami, Dario Spirito
We consider the set of all the ideals of a ring, endowed with the coarse lower topology. The aim of this paper is to study the topological properties of distinguished subspaces of…
Radical semistar operations
Dario Spirito
We introduce and study the set of radical stable operations of an integral domain . We show that their set is a complete lattice that is the join-completion of the set of spectr…
Localizations of integer-valued polynomials and of their Picard group
Dario Spirito
We prove a necessary and sufficient criterion for the ring of integer-valued polynomials to behave well under localization. Then, we study how the Picard group of …
Almost Dedekind domains without radical factorization
Dario Spirito
We study almost Dedekind domains with respect to the failure of ideals to have radical factorization, that is, we study how to measure how far an almost Dedekind domain is from bei…
The polynomial closure is not topological
Giulio Peruginelli, Dario Spirito
We characterize the polynomial closure of a pseudo-convergent sequence in a valuation domain of arbitrary rank, and then we use this result to show that the polynomial closure…
The derived sequence of a pre-Jaffard family
Dario Spirito
We introduce the concept of \emph{pre-Jaffard family}, a generalization of Jaffard families obtained by substituting the locally finite hypothesis with a much weaker compactness hy…
Metrizability of spaces of valuation domains associated to pseudo-convergent sequences
Giulio Peruginelli, Dario Spirito
Let be a valuation domain of rank one with quotient field . We study the set of extensions of to the field of rational functions induced by pseudo-convergent sequ…
Asymptotic for the number of star operations on one-dimensional Noetherian domains
Dario Spirito
We study the set of star operations on local Noetherian domains of dimension such that the conductor (where is the integral closure of ) is equal to the maxi…
Isolated points of the Zariski space
Dario Spirito
Let be an integral domain and be a field containing . We study the isolated points of the Zariski space , with respect to the constructible topology.…
Radicals of principal ideals and the class group of a Dedekind domain
Dario Spirito
For a Dedekind domain , let be the set of ideals of that are radical of a principal ideal. We show that, if are Dedekind domains and there is an orde…
The Golomb space is topologically rigid
Taras Banakh, Dario Spirito, Sławomir Turek
The is the set of positive integers endowed with the topology generated by the base consisting of arithmetic progressions $\{a+bn:n\g…
The Golomb topology of polynomial rings
Dario Spirito
We study properties of the Golomb topology on polynomial rings over fields, in particular trying to determine conditions under which two such spaces are not homeomorphic. We show t…
Multiplicative closure operations on ring extensions
Dario Spirito
Let be a ring extension and be a set of -submodules of . We introduce a class of closure operations on (which we call \emph{multipl…
The Golomb topology on a Dedekind domain and the group of units of its quotients
Dario Spirito
We study the Golomb spaces of Dedekind domains with torsion class group. In particular, we show that a homeomorphism between two such spaces sends prime ideals into prime ideals an…
Suprema in spectral spaces and the constructible closure
Carmelo Antonio Finocchiaro, Dario Spirito
Given an arbitrary spectral space , we endow it with its specialization order and we study the interplay between suprema of subsets of and the constructible to…
Extending valuations to the field of rational functions using pseudo-monotone sequences
Giulio Peruginelli, Dario Spirito
Let be a valuation domain with quotient field . We show how to describe all extensions of to when the -adic completion is algebraically closed, g…
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…