Module on Cartesian Product is Module/Proof 3

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Theorem

Let $\struct {R, +_R, \times_R}$ be a ring.

Let $n \in \N_{>0}$.


Let $\struct {R^n, +, \times}_R$ be the $R$-module $R^n$.


Then $\struct {R^n, +, \times}_R$ is an $R$-module.


Proof

This is a special case of a Finite Direct Product of Modules is Module where each of the $G_k$ is the $R$-module $R$.

$\blacksquare$