Mappings to R-Algebraic Structure form Similar R-Algebraic Structure

Theorem
Let $X$ be a nonempty set, and let $R$ be a ring.

Let $\struct {G, \circ}_R$ be an $R$-algebraic structure.

Let $G^X$ be the set of all mappings from $X$ to $G$.

Denote also by $\circ$ the binary operation defined on $G^X$ by pointwise ($R$)-scalar multiplication.

Also see

 * Mappings to Algebraic Structure form Similar Algebraic Structure