Right Ideal is Right Module over Ring/Ring is Right Module over Ring
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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 $\struct {R, +, \times}$.
$\blacksquare$
Also see
Sources
- 2003: P.M. Cohn: Basic Algebra: Groups, Rings and Fields ... (next): Chapter $4$: Rings and Modules: $\S 4.1$: The Definitions Recalled