Perinormality -- a generalization of Krull domains

TL;DR

This paper introduces perinormal domains, a new class of integral domains that generalize Krull domains, with characterizations and examples across algebra, geometry, and number theory.

Contribution

It defines perinormality, explores its properties, and relates it to divisor class groups, expanding the understanding of domain classifications.

Findings

Perinormal domains are strictly between Krull and weakly normal domains.

Equivalent characterizations are provided for universally catenary domains.

Examples illustrate the concepts in algebra, geometry, and number theory.

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.