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

• Results about Module on Cartesian Product can be found here.