Definition:Monoid Ring/Canonical Mapping

Definition
Let $R$ be a ring with unity.

Let $\struct {G, *}$ be a monoid with identity element $1$.

Let $R \sqbrk G$ be the monoid ring of $G$ over $R$. Let $e_1$ be the canonical basis element.

The canonical mapping to $R \sqbrk G$ is the mapping $R \to R \sqbrk G$ which sends $r$ to $r * e_1$.

Also see

 * Canonical Embedding in Monoid Ring is Unital Ring Monomorphism