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.

substantial changes due to comments from several people including the referee (cf. acknowledgments). Among other things, universal catenarity is necessary for the main theorem of section 4, and we have new characterizations of both perinormality and global perinormality in terms of flatness of overrings. 20 pages