Definition:Module Structure of Polynomial Ring

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

Let $R[X]$ be a polynomial ring in one variable $X$ over $R$.

The $R$-module structure on $R[X]$ is the module structure as an algebra over $R$.

Also see

 * Monomials form Basis of Polynomial Ring

Generalizations

 * Definition:Module Structure of Algebra over Ring
 * Definition:Restriction of Scalars of Module