Definition:Ring of Mappings/Commutativity

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

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

From Structure Induced by Commutative Ring is a Commutative Ring, the ring of mappings from $S$ to $R$ is a commutative ring.

Also see

 * Structure Induced by Ring Operations is Ring


 * Structure Induced by Commutative Ring Operations is Commutative Ring