Definition:Ring of Mappings/Unity

Definition

Let $\struct {R, +, \circ}$ be a ring with unity whose unity is $1$.

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 Operations is Ring with Unity, the ring of mappings from $S$ to $R$ is a ring with unity whose unity is the constant mapping $f_1: S \to R$ defined as:

$\quad \forall s \in S : \map {f_1} x = 1$

Also see

• Structure Induced by Ring Operations is Ring

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