Definition:Additive Group of Ring

Definition
Let $\left({R, +, \circ}\right)$ be a ring.

The group $\left({R, +}\right)$ is known as the additive group of $R$.

Additive Group is Abelian
Most treatments of this subject include as an axiom that the additive group of a ring is abelian.

This is true, and can be proved directly from the other axioms.

Also denoted as
Some sources write $\left({R, +}\right)$ as $R^+$ but this can be confused with the set of positive elements $R_+$ of an ordered ring.