Multiple Function on Ring is Homomorphism

Theorem
Let $\struct {R, +, \circ}$ be a ring.

Let $g_a: \Z \to R$ be the mapping from the integers into $R$ defined as:
 * $\forall n \in \Z:\forall a \in R: \map {g_a} n = n \cdot a$

where $\cdot$ denotes the multiple operation.

Then:
 * $g_a$ is a group homomorphism from $\struct {\Z, +}$ to $\struct {R, +}$.