\begin{definition}[Definition:Ring of Mappings]
Let $\struct {R, +, \circ}$ be a ring.
Let $S$ be a set.
Let $R^S$ be the set of all mappings from $S$ to $R$.
The '''ring of mappings''' from $S$ to $R$ is the algebraic structure $\struct {R^S, +', \circ'}$ where $+'$ and $\circ'$ are the (pointwise) operations induced on $R^S$ by $+$ and $\circ$.
From Structure Induced by Ring Operations is Ring, $\struct {R^S, +', \circ'}$ is a ring.
\end{definition}