Komoto, Susumu; Watanabe, Toru Presheaves associated to modules over subrings of Dedekind domains. (English) Zbl 0956.13003 Tokyo J. Math. 22, No. 2, 341-351 (1999). 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. Reviewer: Christodor-Paul Ionescu (Bucureşti) Cited in 2 Documents MSC: 13F05 Dedekind, Prüfer, Krull and Mori rings and their generalizations 14A05 Relevant commutative algebra Keywords:presheaves; sheaves; Dedekind domains PDFBibTeX XMLCite \textit{S. Komoto} and \textit{T. Watanabe}, Tokyo J. Math. 22, No. 2, 341--351 (1999; Zbl 0956.13003) Full Text: DOI