\begin{definition}[Definition:Free Module on Set/Canonical Mapping]
Let $R$ be a ring with unity.
Let $I$ be a set.
Let $R^{(I)}$ be the free $R$-module on $I$.
The '''canonical mapping''' $I \to R^{(I)}$ is the mapping that sends $i \in I$ to the $i$th standard basis element $e_i$.
\end{definition}