Definition:Ring of Sequences/Unity

Definition
Let $\struct {R, +, \circ}$ be a ring with unity $1$. Let $\struct {R^\N, +', \circ'}$ be the ring of sequences over $R$.

From Structure Induced by Ring with Unity Operations is 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