Abstract
The class of Matlis domain, those integral domains whose quotient field has projective dimension 1, is surprisingly broad. However, whether every domain of Krull dimension 1 is a Matlis domain does not appear to have been resolved in the literature. In this note we construct a class of examples of one-dimensional domains (in fact, almost Dedekind domains) that are overrings of K(X;Y ) but are not Matlis domains. These examples fit into a larger context of what we term of Noetherian domains, a notion we also consider briefly, and with emphasis on Prufer sections of two-dimensional Noetherian domains.
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