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Globalizing local properties of Prüfer domains. (English) Zbl 0928.13013
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.

13G05 Integral domains
13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations
13B30 Rings of fractions and localization for commutative rings
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