Definition:Ring of Sequences/Zero

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

Let $\struct {R^\N, +', \circ'}$ be the ring of sequences from the natural numbers $\N$ to $R$.

The zero of the ring of sequences is the constant sequence $\tuple{0,0,0,\dots}$, where $0$ is the zero in $R$.

Also see

 * Structure Induced by Ring Operations is Ring