Module is Submodule of Itself

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 $27.1$
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