\begin{definition}[Definition:Additive Subgroup]
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 ''' $\struct {R, +, \times}$.
\end{definition}