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

$\blacksquare$

Also see

• Ideal is Bimodule over Ring

Sources

• 2003: P.M. Cohn: Basic Algebra: Groups, Rings and Fields ... (previous) ... (next): Chapter $4$: Rings and Modules: $\S 4.1$: The Definitions Recalled