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 t-ideals have Prufer integral closure. We also prove that the UMT-property is preserved upon passage to polynomial rings. Finally, we characterize the UMT-property in certain pullback constructions; as an application, we show that a domain has Prufer integral closure if and only if all its overrings are UMT-domains.
Fontana, M., Gabelli, S., Houston, E. (1998). UMT-domains and domains with Prüfer integral closure. COMMUNICATIONS IN ALGEBRA, 26(4), 1017-1039 [10.1080/00927879808826181].
UMT-domains and domains with Prüfer integral closure
FONTANA, Marco;GABELLI, Stefania;
1998-01-01
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 t-ideals have Prufer integral closure. We also prove that the UMT-property is preserved upon passage to polynomial rings. Finally, we characterize the UMT-property in certain pullback constructions; as an application, we show that a domain has Prufer integral closure if and only if all its overrings are UMT-domains.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
