Ideal is Bimodule over Ring/Ring is Bimodule over Ring

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

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

Proof
From Ring is Ideal of Itself and Ideal is Bimodule over Ring, $\struct {R, +, \times, \times}$ is a bimodule over $\struct {R, +, \times}$.

Also see

 * Ideal is Bimodule over Ring