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 $R \sqbrk \N$ be the monoid ring of $\N$ over $R$.

The polynomial ring over $R$ is the ordered triple $\struct {R \sqbrk \N, \iota, X}$ where:


 * $X \in R \sqbrk \N$ is the standard basis element associated to $1 \in \N$
 * $\iota : R \to R \sqbrk \N$ is the canonical mapping.

Also see

 * Equivalence of Definitions of Polynomial Ring