Definition:Polynomial Ring/Monoid Ring on Free Monoid on Set

Definition
Let $R$ be a commutative ring with unity.

Let $I$ be a set. Let $R \sqbrk {\family {X_i: i \in I} }$ be the ring of polynomial forms in $\family {X_i: i \in I}$.

The polynomial ring in $I$ indeterminates over $R$ is the ordered triple $\struct {\struct {A, +, \circ}, \iota, \family {X_i: i \in I} }$

Also see

 * Equivalence of Definitions of Polynomial Ring