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 Trivial Subgroup is a subgroup of $$\left({G, +_G}\right)$$.