Globalizing local properties of Prüfer domains (Q1270382)

A property \({\mathcal P}\) is called a globalizing property for a class \({\mathcal C}\) of integral domains if the property \({\mathcal P}\) holds for each localization \(R_M\) of an \(R\) in \({\mathcal C}\) at each maximal ideal \(M\) of \(R\). In this paper, the author studies several globalizing properties for different classes of Prüfer domains with particular emphasis on when local divisoriality and invertibility properties can be globalized. Some of the properties and classes of Prüfer domains studied include \(SV\)-stable domains, \(h\)-local domains, divisorial and totally divisorial domains, property \((\# \#)\), and strongly discrete Prüfer domains.