\begin{definition}[Definition:Monomial of Polynomial Ring/Multiple Variables]
Let $R$ be a commutative ring with unity.
Let $I$ be a set.
Let $R \sqbrk {\family {X_i}_{i \mathop \in I} }$ be a polynomial ring in $I$ variables $\family {X_i}_{i \mathop \in I}$.
Let $y \in R \sqbrk {\family {X_i}_{i \mathop \in I} }$.
A '''monomial''' of $R \sqbrk {\family {X_i}_{i \mathop \in I} }$ is an element that is a product of variables; specifically:
\end{definition}