Definition:Monoid Ring/Canonical Mapping

Definition
Let $R$ be a ring with unity.

Let $G$ be a monoid with identity element $1$.

Let $R[G]$ be the monoid ring of $G$ over $R$. Let $e_1$ be the canonical basis element.

The canonical mapping to $R[G]$ is the mapping $R\to R[G]$ which sends $r$ to $r\cdot e_1$.

Also see

 * Canonical Embedding in Monoid Ring is Unital Ring Monomorphism