Fractional ideal

Summary

A fractional ideal of an integral domain $R$ is a subset of its field of fractions. After clearing denominators, it becomes an ideal of $R$. Fractional ideals can be multiplied, and in a Dedekind domain every nonzero fractional ideal has an inverse. So the nonzero fractional ideals of a Dedekind domain form a group, and its quotient by the principal ones is the ideal class group.