\begin{definition}[Definition:Polynomial over Ring as Sequence]
Let $R$ be a commutative ring with unity.
A '''polynomial''' over $R$ can be defined as a sequence in $R$ whose domain is $\N$ and which has finite support.
That is, it is an element of the ring of sequences of finite support.
Because a field is a commutative ring with unity, this applies in particular to a field.
\end{definition}