Module is Submodule of Itself
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Theorem
Let $\struct {G, +_G, \circ}_R$ be an $R$-module.
Then $\struct {G, +_G, \circ}_R$ is a submodule of itself.
Proof
Follows directly from Group is Subgroup of Itself.
$\blacksquare$
Sources
- 1965: Seth Warner: Modern Algebra ... (previous) ... (next): Chapter $\text {V}$: Vector Spaces: $\S 27$. Subspaces and Bases: Example $27.1$