Monomials form Basis of Polynomial Ring

Theorem

One Variable

Let $R$ be a commutative ring with unity.

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

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

Multiple Variables

Monomials form Basis of Polynomial Ring/Multiple Variables

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Also see

• Definition:Coefficient of Polynomial
• Equality of Monomials of Polynomial Ring