Invertible ideal

Summary

An invertible ideal of an integral domain $R$ is a fractional ideal $I$ that has an inverse $J$ with $IJ = R$. Fractional ideals are $R$-submodules of the field of fractions that become ordinary ideals after clearing one denominator. The invertible fractional ideals form a group under multiplication, and its quotient by the principal ones is the Picard group of $R$. A Dedekind domain is exactly a domain in which every nonzero fractional ideal is invertible.