Definition:Ring of Mappings/Unity

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

Let $S$ be a set.

Let $\struct {R^S, +', \circ'}$ be the ring of mappings from $S$ to $R$.

From Structure Induced by Ring with Unity is a Ring with Unity, if $R$ is a ring with unity then the ring of mappings from $S$ to $R$ is a ring with unity; namely the constant mapping $f_1 : S \to R$, where:
 * $\quad 1$ is the unity in $R$
 * $\quad \forall s \in S : \map {f_1} x = 1$

Also see

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