If is a maximal order, i.e., the ring of integers of , then every fractional ideal of is invertible and the Picard group of is the class group of . The order of the Picard group of is sometimes called the class number of . If is maximal, then the order of the Picard group is equal to the class number of .
See alsoAlgebraic Number Theory, Class Group, Class Number, Fractional Ideal, Number Field, Number Field Order
This entry contributed by David Terr