G. Peruginelli

activity

20112026

most citedIntegral-valued polynomials over the set of algebraic integers of bounded degree

18 citations · 206 across the 29 of their papers we have counts for

collaborators

29 papers

math.AC2026

Approximating DVRs by elements of bounded ramification

Gyu Whan Chang, Giulio Peruginelli

Let $V$ be a DVR with quotient field $K$ and perfect residue field, $v$ be the valuation on $K$ associated with $V$ , $K$ be the completion of $K$ , and $K$ be the…

math.AC2026

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 $Z [X]$ and $Q [X]$ . We accomplish this result by classifying the K…

math.RA2025

A classification of Prufer domains of integer-valued polynomials on algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be an integrally closed domain with quotient field $K$ and $A$ a torsion-free $D$ -algebra that is finitely generated as a $D$ -module and such that $A \cap K = D$ . We give a co…

math.NT2024

Nontriviality of rings of integral-valued polynomials

Giulio Peruginelli, Nicholas J. Werner

Let $S$ be a subset of $Z$ , the ring of all algebraic integers. A polynomial $f \in Q [X]$ is said to be integral-valued on $S$ if $f(s) \in \overline{\ma…

math.AC2024

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 $μ$ of $K (x)$ , in terms of (ultrametric) balls in the algebra…

math.NT2023★ 1 cited

Stacked Pseudo-Convergent Sequences and Polynomial Dedekind Domains

Giulio Peruginelli

Let $p \in Z$ be a prime, $Q_{p}$ a fixed algebraic closure of the field of $p$ -adic numbers and $Z_{p}$ the absolute integral closure of th…

math.AC2022★ 7 cited

Polynomial Dedekind domains with finite residue fields of prime characteristic

Giulio Peruginelli

We show that every Dedekind domain $R$ lying between the polynomial rings $Z [X]$ and $Q [X]$ with the property that its residue fields of prime characteristic are fi…

math.AC2021

The polynomial closure is not topological

Giulio Peruginelli, Dario Spirito

We characterize the polynomial closure of a pseudo-convergent sequence in a valuation domain $V$ of arbitrary rank, and then we use this result to show that the polynomial closure…

math.AC2020

Metrizability of spaces of valuation domains associated to pseudo-convergent sequences

Giulio Peruginelli, Dario Spirito

Let $V$ be a valuation domain of rank one with quotient field $K$ . We study the set of extensions of $V$ to the field of rational functions $K (X)$ induced by pseudo-convergent sequ…

math.NT2020

On the Lucas and Lehmer sequences in Dedekind domains

Xiumei Li, Giulio Peruginelli, Min Sha

In this paper, we first obtain the strong divisibility property for the Lucas and Lehmer sequences in Dedekind domains, and then establish analogues of Zsigmondy's theorem and the…

math.RA2019★ 16 cited

Extending valuations to the field of rational functions using pseudo-monotone sequences

Giulio Peruginelli, Dario Spirito

Let $V$ be a valuation domain with quotient field $K$ . We show how to describe all extensions of $V$ to $K (X)$ when the $V$ -adic completion $K$ is algebraically closed, g…

math.AC2018★ 9 cited

The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences

Giulio Peruginelli, Dario Spirito

Let $V$ be a valuation domain with quotient field $K$ . Given a pseudo-convergent sequence $E$ in $K$ , we study two constructions associating to $E$ a valuation domain of $K (X)$ lyi…

math.AC2017★ 13 cited

Prüfer intersection of valuation domains of a field of rational functions

Giulio Peruginelli

Let $V$ be a rank one valuation domain with quotient field $K$ . We characterize the subsets $S$ of $V$ for which the ring of integer-valued polynomials ${\rm Int}(S,V)=\{f\in K[X]…

math.AC2016★ 10 cited

Transcendental extensions of a valuation domain of rank one

Giulio Peruginelli

Let $V$ be a valuation domain of rank one and quotient field $K$ . Let $K^$ be a fixed algebraic closure of the $v$ -adic completion $K^$ of $K$ and let $\overlin…

math.RA2016★ 8 cited

Decomposition of integer-valued polynomial algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be a commutative domain with field of fractions $K$ , let $A$ be a torsion-free $D$ -algebra, and let $B$ be the extension of $A$ to a $K$ -algebra. The set of integer-valued…

math.RA2016★ 12 cited

Non-triviality Conditions for Integer-valued Polynomial Rings on Algebras

G. Peruginelli, N. J. Werner

Let $D$ be a commutative domain with field of fractions $K$ and let $A$ be a torsion-free $D$ -algebra such that $A \cap K = D$ . The ring of integer-valued polynomials on $A$ with c…

math.NT2015★ 10 cited

Adelic versions of the Weierstrass approximation theorem

Jean-Luc Chabert, Giulio Peruginelli

Let $E = \prod_{p \in P} E_{p}$ be a compact subset of $Z = \prod_{p \in P} Z_{p}$ and denote by $\mathcal C(\underline{E},\widehat{\mat…

math.NT2015★ 8 cited

Galois structure on integral valued polynomials

Bahar Heidaryan, Matteo Longo, Giulio Peruginelli

We characterize finite Galois extensions $K$ of the field of rational numbers in terms of the rings $Int_{Q} (O_{K})$ , recently introduced by Loper and Werner,…

math.RA2015★ 17 cited

Properly Integral Polynomials over the Ring of Integer-valued Polynomials on a Matrix Ring

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be a domain with fraction field $K$ , and let $M_{n} (D)$ be the ring of $n \times n$ matrices with entries in $D$ . The ring of integer-valued polynomials on the matrix ring $M…

math.AC2015★ 12 cited

Polynomial overrings of $Int (Z)$

Jean-Luc Chabert, Giulio Peruginelli

We show that every polynomial overring of the ring $Int (Z)$ of polynomials which are integer-valued over $Z$ may be considered as the ring of polynomials whic…

math.AC2015★ 2 cited

The lattice of primary ideals of orders in quadratic number fields

Giulio Peruginelli, Paolo Zanardo

Let $O$ be an order in a quadratic number field $K$ with ring of integers $D$ , such that the conductor $F = f D$ is a prime ideal of $O$ , where $f \in Z$ is a prime…

math.RA2014★ 4 cited

Idempotent pairs and PRINC domains

Giulio Peruginelli, Luigi Salce, Paolo Zanardo

A pair of elements $a, b$ in an integral domain $R$ is an idempotent pair if either $a (1 - a) \in b R$ , or $b (1 - b) \in a R$ . $R$ is said to be a PRINC domain if all the ideals generated…

math.RA2014★ 13 cited

The ring of polynomials integral-valued over a finite set of integral elements

G. Peruginelli

Let $D$ be an integral domain with quotient field $K$ and $Ω$ a finite subset of $D$ . McQuillan proved that the ring $Int (Ω, D)$ of polynomials in $K [X]$ which are integer-val…

math.AC2014★ 15 cited

Integral closure of rings of integer-valued polynomials on algebras

Giulio Peruginelli, Nicholas J. Werner

Let $D$ be an integrally closed domain with quotient field $K$ . Let $A$ be a torsion-free $D$ -algebra that is finitely generated as a $D$ -module. For every $a$ in $A$ we consider i…

Approximating DVRs by elements of bounded ramification

Geometric configuration of integrally closed Noetherian domains

A classification of Prufer domains of integer-valued polynomials on algebras

Nontriviality of rings of integral-valued polynomials

A topological approach to key polynomials

Stacked Pseudo-Convergent Sequences and Polynomial Dedekind Domains

Polynomial Dedekind domains with finite residue fields of prime characteristic

The polynomial closure is not topological

Metrizability of spaces of valuation domains associated to pseudo-convergent sequences

On the Lucas and Lehmer sequences in Dedekind domains

Extending valuations to the field of rational functions using pseudo-monotone sequences

The Zariski-Riemann space of valuation domains associated to pseudo-convergent sequences

Prüfer intersection of valuation domains of a field of rational functions

Transcendental extensions of a valuation domain of rank one

Decomposition of integer-valued polynomial algebras

Non-triviality Conditions for Integer-valued Polynomial Rings on Algebras

Adelic versions of the Weierstrass approximation theorem

Galois structure on integral valued polynomials

Properly Integral Polynomials over the Ring of Integer-valued Polynomials on a Matrix Ring

Polynomial overrings of Int(Z)

The lattice of primary ideals of orders in quadratic number fields

Idempotent pairs and PRINC domains

The ring of polynomials integral-valued over a finite set of integral elements

Integral closure of rings of integer-valued polynomials on algebras

Polynomial overrings of $Int (Z)$