Monomials form Basis of Polynomial Ring/One Variable

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

Let $R \sqbrk X$ be a polynomial ring over $R$ in the variable $X$.

Then the mononomials of $R \sqbrk X$ are a basis of $R \sqbrk X$ as a module over $R$.

Proof
Follows from:
 * Polynomial is Linear Combination of Mononomials
 * Mononomials of Polynomial Ring are Linearly Independent