Abstract
Let R be an integral domain, X( R) the abstract Riemann surface of R, and ( R′) b the Kronecker function ring of the integral closure R′ of R. It is proved that there exists a homeomorphism, natural in R, between X( R) and Spec(( R′) b ). Ideal-theoretic and topological results are given for the extension j: R ▪(R ′) b , notably that R is a Prüfer domain if and only if R = R′ and j is universally going-down. It is also proved that each spectral space X is a closed spectral image of a treed spectral space Y; if X is irreducible, Y can be taken as an abstract Riemann surface.
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