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 $\struct {R, +, \times}$.

Sources

• 1970: B. Hartley and T.O. Hawkes: Rings, Modules and Linear Algebra ... (previous) ... (next): $\S 2.1$: Subrings: Notation $1$