On locally divided domains of the form Int(\(D\))
Here is the authors' abstract: ``Let \(D\) be an integral domain which is not a field. If either \(D\) is Noetherian or \(D\) is a Prüfer domain, then Int\((D)\), the ring of integer-valued polynomials of \(D\), is a treed domain if and only if it is a going-down domain. Suppose henceforth that \((D,m)\) is Noetherian local and one-dimensional, with \(D/ m\) finite. Then Int\((D)\) is a going-down domain if and only if \(D\) is unibranched (inside its integral closure); and Int\((D)\) is locally divided if and only if \(D\) is analytically irreducible. Thus, if \(D\) is unibranched but not analytically irreducible, then Int\((D)\) provides an example of a two-dimensional going-down domain which is not locally divided. Also, Int\((D)\) is a locally pseudo-valuation domain if and only if \(D\) is itself a pseudo-valuation domain. Thus, Int\((D)\) also provides an example of a two-dimensional locally divided domain which is not an LPVD.'' LPVDs (locally pseudovaluation domains), locally divided domains, etc., are generalizations of Prüfer domains.
scientific article; zbMATH DE number 1449198