# Category:Rings of Sequences

Let $\struct {R, +, \circ}$ be a ring.
Given the natural numbers $\N$, the ring of sequences over $R$ is the ring of mappings $\struct {R^\N, +', \circ'}$ where:
$(1): \quad R^\N$ is the set of sequences in $R$
$(2): \quad +'$ and $\circ'$ are the (pointwise) operations induced by $+$ and $\circ$.