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 .

# Class Group

## See also

Class Number, Equivalence Class, Fractional Ideal
*This entry contributed by David Terr*

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## References

Marcus, D. A.*Number Fields, 3rd ed.*New York: Springer-Verlag, 1996.

## Referenced on Wolfram|Alpha

Class Group## Cite this as:

Terr, David. "Class Group." From *MathWorld*--A Wolfram Web Resource, created by Eric W. Weisstein.
https://mathworld.wolfram.com/ClassGroup.html