Definition:Module on Cartesian Product/Special Case

Definition
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 $R$.

Also see

 * Definition:Module on Cartesian Product, of which this is a special case