Right Ideal is Right Module over Ring/Ring is Right Module over Ring

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

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

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

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

Also see

 * Ring is Left Module over Ring