18 citations · 206 across the 29 of their papers we have counts for
14 papers · 1 filter
Approximating DVRs by elements of bounded ramification
Gyu Whan Chang, Giulio Peruginelli
Let be a DVR with quotient field and perfect residue field, be the valuation on associated with , be the completion of , and be the…
Geometric configuration of integrally closed Noetherian domains
Gyu Whan Chang, Giulio Peruginelli
In this paper, we completely describe the family of integrally closed Noetherian domains between and . We accomplish this result by classifying the K…
A topological approach to key polynomials
Enric Nart, Josnei Novacoski, Giulio Peruginelli
In this paper we present characterizations of the sets of key polynomials and abstract key polynomials for a valuation of , in terms of (ultrametric) balls in the algebra…
Polynomial Dedekind domains with finite residue fields of prime characteristic
Giulio Peruginelli
We show that every Dedekind domain lying between the polynomial rings and with the property that its residue fields of prime characteristic are fi…
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…
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…
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…
Prüfer intersection of valuation domains of a field of rational functions
Giulio Peruginelli
Let be a rank one valuation domain with quotient field . We characterize the subsets of for which the ring of integer-valued polynomials ${\rm Int}(S,V)=\{f\in K[X]…
Transcendental extensions of a valuation domain of rank one
Giulio Peruginelli
Let be a valuation domain of rank one and quotient field . Let be a fixed algebraic closure of the -adic completion of and let $\overlin…
Polynomial overrings of
Jean-Luc Chabert, Giulio Peruginelli
We show that every polynomial overring of the ring of polynomials which are integer-valued over may be considered as the ring of polynomials whic…
The lattice of primary ideals of orders in quadratic number fields
Giulio Peruginelli, Paolo Zanardo
Let be an order in a quadratic number field with ring of integers , such that the conductor is a prime ideal of , where is a prime…
Integral closure of rings of integer-valued polynomials on algebras
Giulio Peruginelli, Nicholas J. Werner
Let be an integrally closed domain with quotient field . Let be a torsion-free -algebra that is finitely generated as a -module. For every in we consider i…
Factorization of integer-valued polynomials with square-free denominator
Giulio Peruginelli
We describe an algorithm to compute the essentially different factorizations of a given image primitive integer-valued polynomial $f(X)=g(X)/d\in\Q[X]$, where and $d\in…
Primary decomposition of the ideal of polynomials whose fixed divisor is divisible by a prime power
Giulio Peruginelli
We characterize the fixed divisor of a polynomial in by looking at the contraction of the powers of the maximal ideals of the overring ${\rm Int}(\mathbb{Z})…