Definition:Polynomial Ring/Monoid Ring on Natural Numbers

Definition
Let $R$ be a commutative ring with unity. Let $\N$ denote the additive monoid of natural numbers.

Let $R[\N]$ monoid ring of $\N$ over $R$.

The polynomial ring over $R$ is the ordered triple $(R[\N], f, X)$

where:


 * $X \in R[\N]$ is the standard basis element associated to $1\in \N$.
 * $f : R \to R[\N]$ is the canonical mapping.