Residual functions and divisorial ideals

TL;DR

This paper introduces residual functions on topological spaces to analyze the structure of divisorial ideals in Prüfer domains, providing new insights into their algebraic properties.

Contribution

It defines residual functions and applies this concept to study the freeness of divisorial ideal groups in Prüfer domains, offering a novel approach.

Findings

Residual functions characterize certain topological properties.

Freeness of divisorial ideal groups can be studied via residual functions.

New connections between topology and algebra in Prüfer domains.

Abstract

We define a \emph{residual function} on a topological space $X$ as a function $f:X\longrightarrow\mathbb{Z}$ such that $f^{-1}(0)$ contains an open dense set, and we use this notion to study the freeness of the group of divisorial ideals on a Pr\"ufer domain.