Definition:Constant Polynomial

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

Let $\left({S, +, \circ}\right)$ be a subring of $R$.

For arbitrary $x \in R$, let $S \left[{x}\right]$ be the set $S \left[{x}\right]$ be the set of polynomials in $x$ over $S$.

Let $\displaystyle f = \sum_{i \mathop = 0}^n a_i \circ x^i \in S \left[{x}\right]$ such that:
 * $\forall i \in \Z: i > 0: a_i = 0$

Then $f$ is a constant polynomial.

That is:

Also see

 * Definition:Constant