UMT-DOMAINS AND DOMAINS WITH PRUFER INTEGRAL CLOSURE

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 i f its localizations at maximal t-ideals have Prufer integral closure. We also prove that the UMT-property is preserved upon passage to polyn omial rings. Finally, we characterize the UMT-property in certain pull back constructions; as an application, we show that a domain has Prufe r integral closure if and only if all its overrings are UMT-domains.