# Definition:Product of Fractional Ideals

## Definition

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:

$\left\{ \displaystyle\sum_{i = 1}^r a_i b_i : a_i \in I, b_i \in J, r \in \N \right\}$