Definition:Additive Subgroup

Definition
Let $\left({R, +, \times}\right)$ be a ring.

Let $\left({R, +}\right)$ be the additive group of $\left({R, +, \times}\right)$.

Let $\left({S, +}\right)$ be a subgroup of $\left({R, +}\right)$

Then $\left({S, +}\right)$ is an additive subgroup of  $\left({R, +, \times}\right)$.