Definition:Monomial of Polynomial Ring/Multiple Variables

Definition
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 $(X_i)_{i\in I}$.

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:

Also see

 * Equivalence of Definitions of Monomial of Polynomial Ring in Multiple Variables