Pole assignability and the invariant factor theorem in Prüfer domains and Dedekind domains (Q1112117)

The authors investigate pole assignability property (PA-property) and its stronger form called the GCU-property in Prüfer and Dedekind domains. They prove that a Dedekind domain has the GCU-property if and only if it has a torsion free Picard group. In the process of proving this theorem they determine those Prüfer domains satisfying the ``invariant factor theorem''. As a corollary it is shown that if \(R\) is a commutative ring with the property that each nonzero element of \(R\) belongs to only finitely many maximal ideals, then \(R\) has the PA-property.