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

## 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 $\struct {R, +, \times}$.

$\blacksquare$