\begin{definition}[Definition:Monoid Ring/Canonical Mapping]
Let $R$ be a ring with unity.
Let $\left({G, *}\right)$ be a monoid with identity element $1$.
Let $R \left[{G}\right]$ be the monoid ring of $G$ over $R$.
Let $e_1$ be the canonical basis element.
The '''canonical mapping to $R \left[{G}\right]$''' is the mapping $R \to R \left[{G}\right]$ which sends $r$ to $r * e_1$.
\end{definition}