Perinormality – a generalization of Krull domains

Abstract

We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give equivalent characterizations of perinormality. (Later on, we point out some subtleties that occur only in the non-Noetherian context.) We also introduce and explore briefly the related concept of global perinormality, including a relationship with divisor class groups. Throughout, we provide illuminating examples from algebra, geometry, and number theory.