Let $R$ be a ring and $A$ be a non-empty set. $\fun(A,R)$ is a ring with addition and multiplication defined by
\[\begin{align*} f+g &: a\mapsto f(a)+g(a), \\ f\cdot g &: a\mapsto f(a)\cdot g(a) \end{align*}\]for all $f$, $g\in\fun(A,R)$. The neutral elements are
\[\underline{0} : a\mapsto 0, \quad \underline{1} : a\mapsto 1.\]