Presheaves associated to modules over subrings of Dedekind domains (Q1970879)

Let \(A\) be a commutative ring with unit. For \(E\subseteq \text{Spec} A\) let \(S_E= \bigcap_{P\in E}(A-P)\). If \(M\) is an \(A\)-module and \(U\) is an open subset of \(\text{Spec} A\), let \(\overline M(U)=S_U^{-1}M\). In general \(\overline M\) is not a sheaf. The paper deals with the question when \(\overline M\) is actually a sheaf. Several characterizations for rings with the property that \(\overline M\) is a sheaf for any \(A\)-module \(M\), are given. It is also shown that the rings of algebraic integers with quadratic quotient field have this property.