G. Peruginelli

collaborators

6 papers

math.RA2026

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.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.AC2026

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 $I^¼$ of $K (x)$ , in terms of (ultrametric) balls in the algebr…

math.NT2025

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.NT2025

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.NT2025

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…