“Ideals of rings of integer-valued polynomials: a topological approach”
Giovedì 29 Febbraio 2024, ore 16:00 - Aula 1BC45 - Carmelo Finocchiaro (Università di Catania)
Abstract
Let $D$ be a Dedekind domain with finite residue fields and quotient field $K$ and let $$\mathrm {Int(} D \mathrm ) := \{f(T) \in K[T] \:\:|f(D) \subseteq D \;\}$$ be the ring of integer-valued polynomials over $D$. Under such assumptions $\mathrm {Int(} D \mathrm )$ is a two-dimensionaal Prüfer domain whose prime ideals are well-known.
The aim of this talk, based on a paper jointly written with K.A. Loper, is to provide a topological description of some classes of invertible or divisorial ideals of $\mathrm {Int(} D \mathrm )$. As an application of the general theory, we provide examples of divisorial ideals of $\mathrm {Int(} \mathbb Z \mathrm )$ that are not finitely generated.
