\begin{definition}[Definition:Polynomial Ring/Sequences]
Let $R$ be a commutative ring with unity.
Let $R^{\left({\N}\right)}$ be the ring of sequences of finite support over $R$.
Let $\iota : R \to R^{\left({\N}\right)}$ be the mapping defined as:
:$\iota \left({r}\right) = \left \langle {r, 0, 0, \ldots}\right \rangle$.
Let $X$ be the sequence $\left \langle {0, 1, 0, \ldots}\right \rangle$.
{{explain|Please clarify the role of $X$. This does not look like a ring to me. What is the multiplication? --Wandynsky (talk) 17:17, 30 July 2021 (UTC)}}
The '''polynomial ring over $R$''' is the ordered triple $\left({R^{\left({\N}\right)}, \iota, X}\right)$.
\end{definition}