Definition:Fractional Ideal

Let $R$ be an integral domain with field of fractions $K$.
A fractional ideal of $R$ is a subset of $K$ that is a product of an ideal $I$ with the inverse $\lambda^{-1}$ of an element of $R$:
$\lambda^{-1} I = \left\{ {\lambda^{-1} a : a \in I}\right\}$