On a topological characterization of pr\"ufer v-multiplication domains among essential domains

TL;DR

This paper provides a topological characterization of Prüfer v-multiplication domains within essential domains by examining the closure properties of prime ideals in the constructible topology.

Contribution

It introduces a new topological criterion for identifying Prüfer v-multiplication domains among essential domains, linking algebraic and topological properties.

Findings

Prüfer v-multiplication domains are characterized by specific closure properties of prime ideals.

The characterization involves the constructible topology on the prime spectrum.

This approach bridges algebraic properties with topological conditions.

Abstract

In this paper we characterize the Pr\"ufer v-multiplication domain as a class of essential domains verifying an additional property on the closure of some families of prime ideals, with respect to the constructible topology.