\begin{definition}[Definition:Ring of Sequences of Finite Support]
Let $\struct {R, +, \circ}$ be a ring.
Let $P \sqbrk R$ be the set of all sequences in $R$ whose domain is $\N$:
:$P \sqbrk R = \set {\sequence {r_0, r_1, r_2, \ldots} }$
and whose support is finite.
Let the operations $\oplus$ and $\odot$ on $P \sqbrk R$ be defined as follows:
{{:Definition:Operations on Polynomial Ring of Sequences}}
The '''ring of sequences of finite support over $R$''' is the ring $\struct {P \sqbrk R, \oplus, \odot}$.
\end{definition}