Definition:Ring of Sequences/Unity

Note
Let $\struct {R, +, \circ}$ be a ring with unity $1$. Let $\struct {R^\N, +', \circ'}$ be the ring of sequences from the natural numbers $\N$ to $R$.

From Structure Induced by Ring with Unity is a Ring with Unity, the ring of sequences is a ring with unity; namely the constant sequence $\tuple{1,1,1,\dots}$, where $1$ is the unity in $R$.

Also see

 * Structure Induced by Ring Operations is Ring


 * Structure Induced by Ring with Unity Operations is Ring with Unity