Ideal is Bimodule over Ring/Ring is Bimodule over Ring

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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

Sources