Ring is Module over Itself/Proof 2

From ProofWiki
Jump to navigation Jump to search

Theorem

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

Then $\struct {R, +, \circ}_R$ is an $R$-module.


Proof

This is a special case of Module on Cartesian Product is Module:

$\struct {R^n, +, \circ}_R$ is an $R$-module

where $n = 1$.

$\blacksquare$