Let be a number field, then each fractional ideal of belongs to an equivalence class consisting of all fractional ideals satisfying for some nonzero element of . The number of equivalence classes of fractional ideals of is a finite number, known as the class number of . Multiplication of equivalence classes of fractional ideals is defined in the obvious way, i.e., by letting . It is easy to show that with this definition, the set of equivalence classes of fractional ideals form an Abelian multiplicative group, known as the class group of .
See alsoClass Number, Equivalence Class, Fractional Ideal
This entry contributed by David Terr