Definition:Operations on Polynomial Ring of Sequences

Definition
Let $\struct {R, +, \circ}$ be a ring.

Let $P \sqbrk R$ be the set of all sequences in $R$:
 * $P \sqbrk R = \set {\sequence {r_0, r_1, r_2, \ldots} }$

such that each $r_i \in R$, and all but a finite number of terms is zero.

The operations ring addition $\oplus$, ring negative, and ring product $\odot$ on $P \sqbrk R$ are defined as follows:

Also see

 * Polynomial Ring of Sequences is Ring