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  $$\left({R, +, \times}\right)$$.