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

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8 papers · 1 filter

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.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.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.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.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.RA2013★ 15 cited

Integer-valued polynomials over matrices and divided differences

Giulio Peruginelli

Let $D$ be an integrally closed domain with quotient field $K$ and $n$ a positive integer. We give a characterization of the polynomials in $K [X]$ which are integer-valued over the…