Divisor class group

Summary

Let $A$ be a Krull domain. Its divisor class group is the group of formal integer combinations of its height-one primes, modulo the divisors of nonzero fractions. It is trivial exactly when the ring is a unique factorisation domain, so it measures the failure of unique factorization. For a Dedekind domain it is the ideal class group, and it contains the Picard group of the ring.