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

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