Definition:Polynomial over Ring

Definition
Let $R$ be a commutative ring.

Let $D$ be a subring of $R$.

A polynomial in $x$ over $R$ is an element of the form:
 * $P \left({x}\right) = a_n x^n + a_{n-1} x^{n-1} + \cdots + a_a x + a_0$

for some $n \ge 0$ where $x \in R$ and each of the $a_j$ are elements of $D$.

Also see

 * Ring of Polynomial Forms
 * Ring of Polynomial Functions
 * Equality of Polynomials


 * Polynomial Coefficient