Ring is Module over Itself/Proof 2

Theorem
Let $\left({R, +, \circ}\right)$ be a ring.

Then $\left({R, +, \circ}\right)_R$ is an $R$-module.

If $\left({R, +, \circ}\right)$ has a unity, then $\left({R, +, \circ}\right)_R$ is unitary.

Proof
This is a special case of Module on Cartesian Product:
 * $\left({R^n, +, \circ}\right)_R$ is an $R$-module

where $n = 1$.