Definition:Module on Cartesian Product/Special Case
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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.