# Definition:Ring of Sequences/Pointwise Multiplication

## Definition

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

Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.

The pointwise operation $\circ'$ induced by $\circ$ on the ring of sequences is called pointwise multiplication and is defined as:

$\forall \sequence {x_n}, \sequence {y_n} \in R^{\N}: \sequence {x_n} \circ' \sequence {y_n} = \sequence {x_n \circ y_n}$