Definition:Additive Subgroup

Definition
Let $\struct {R, +, \times}$ be a ring.

Let $\struct {R, +}$ be the additive group of $\struct {R, +, \times}$.

Let $\struct {S, +}$ be a subgroup of $\struct {R, +}$

Then $\struct {S, +}$ is an additive subgroup of  $\struct {R, +, \times}$.