Null Module Submodule of All

Theorem

Let $\left({G, +_G, \circ}\right)_R$ be an $R$-module.

Then the null module:

$\left({\left\{{e_G}\right\}, +_G, \circ}\right)_R$

is a submodule of $\left({G, +_G, \circ}\right)_R$.

Proof

Follows directly from the fact that the trivial subgroup is a subgroup of $\left({G, +_G}\right)$.

$\blacksquare$