\begin{definition}[Definition:Product of Fractional Ideals]
Let $R$ be an integral domain with fraction field $K$.
Let $I, J \subseteq K$ be fractional ideals of $R$.
The '''product of $I$ and $J$''' is the set of summations:
:$\ds \set {\sum_{i \mathop = 1}^r a_i b_i : a_i \in I, b_i \in J, r \in \N}$
\end{definition}