Definition:Additive Subgroup
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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 $1$