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Abstract
An integral domain R is said to be a UMT-domain if uppers to zero in R[X) are maximal t-ideals. We show that R is a UMT-domain if and only if its localizations at maximal tdeals have Prüfer integral closure. We also prove that the UMT-property is preserved upon passage to polynomial rings. Finally, we characterize the UMT-property in certian pullback constructions; as an application, we show that a domain has Prüfer integral closure if and only if all its overrings are UMT-domains.
1Partially supported by research funds of Ministero dell’Università e della Ricerca Scientifica e Technologica.
2Supported in part by funds provided by the Consiglio Nazionale delle Ricerche and by the University of North Carolina at Charlotte.
1Partially supported by research funds of Ministero dell’Università e della Ricerca Scientifica e Technologica.
2Supported in part by funds provided by the Consiglio Nazionale delle Ricerche and by the University of North Carolina at Charlotte.
Notes
1Partially supported by research funds of Ministero dell’Università e della Ricerca Scientifica e Technologica.
2Supported in part by funds provided by the Consiglio Nazionale delle Ricerche and by the University of North Carolina at Charlotte.
