Definition:Polynomial Function

Arbitrary Ring
Let $R$ be a commutative ring with unity.

Let the mapping $p: R \to R$ be defined such that there exists a sequence:
 * $\left \langle {\alpha_k} \right \rangle_{k \in \left[{0 \,.\,.\, n}\right]}$

of elements of $R$ such that:
 * $\displaystyle p = \sum_{k \mathop = 0}^n \alpha_k {\operatorname{id}_R}^k$

where $\operatorname{id}_R$ is the identity mapping on $R$.

Then $p$ is known as a polynomial function on $R$ in one variable.

Also see

 * Definition:Ring of Polynomial Functions
 * Definition:Polynomial


 * Polynomial Functions form Submodule of All Functions