Krull domain

Summary

A Krull domain is an integral domain that is the intersection of a family of discrete valuation rings of its fraction field. The family must satisfy a finiteness condition: each nonzero element has nonzero valuation for only finitely many of them. Unique factorisation domains, Dedekind domains and Noetherian integrally closed domains are Krull domains. Krull domains are the natural setting for the divisor class group, which measures their failure to be factorial.