# Noetherian affine schemes for which localization computes the values of the structure sheaf

Is there a non-tautological characterization of the class of commutative unital Noetherian rings satisfying the following property: for any open subset $$U$$ of the topological space of $$\mathrm{Spec}\,R$$, the natural map from the localization of $$R$$ at the multiplicative set of global functions not vanishing anywhere on $$U$$ to $$\mathcal{O}_{\mathrm{Spec}\,R}(U)$$ is an isomorphism? Some interesting sufficient conditions at least?

Note that not all commutative unital Noetherian rings satisfy this property.