The complete integral closure of a Pr\"ufer domain is a topological property

TL;DR

This paper demonstrates that the prime spectrum of the complete integral closure of a Pr"ufer domain can be fully characterized by the Zariski topology of the original domain's spectrum, linking algebraic and topological properties.

Contribution

It establishes a topological criterion for understanding the prime spectrum of the complete integral closure of Pr"ufer domains, connecting algebraic closure with spectral topology.

Findings

Prime spectrum of $D^*$ determined by $ ext{Spec}(D)$ topology.

Complete integral closure preserves spectral topological properties.

Provides a new perspective on the structure of Pr"ufer domains.

Abstract

We show that the prime spectrum of the complete integral closure $D^\ast$ of a Pr\"ufer domain $D$ is completely determined by the Zariski topology on the spectrum $\mathrm{Spec}(D)$ of $D$.