\begin{definition}[Definition:Ring of Polynomial Forms]
Let  $R$ be a  commutative ring with unity.
Let $I$ be a set
Let $\family {X_i: i \in I}$ be an indexed set.
Let $A = R \sqbrk {\family {X_i: i \in I} }$ be the set of all polynomial forms over $R$ in $\family {X_i: i \in I}$.
Let $+$ and $\circ$ denote the standard addition and multiplication of polynomial forms.
The '''ring of polynomial forms''' is the ordered triple  $\struct {A, +, \circ}$.
\end{definition}