Left Ideal is Left Module over Ring/Ring is Left Module over Ring

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Theorem

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


Then $\struct {R, +, \times}$ is a left module over $\struct {R, +, \times}$.


Proof

From Ring is Ideal of Itself, $R$ is a left ideal.

From Left Ideal is Left Module over Ring, $\struct {R, +, \times}$ is a left module over $\struct {R, +, \times}$.

$\blacksquare$

Also see

Sources