\begin{definition}[Definition:Module on Cartesian Product/Special Case]
Let $\struct {R, +_R, \times_R}$ be a ring.
Let $+: R \times R \to R$ be defined as:
:$\alpha + \beta = \alpha +_R \beta$
Let $\times: R \times R \to R$ be defined as:
:$\lambda \times \alpha = \lambda \times_R \alpha$
Then $\struct {R, +, \times}_R$ is '''the $R$-module $R$'''.
\end{definition}