Definition:Additive Group of Ring

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

The group $\struct {R, +}$ is known as the additive group of $R$.

Also defined as

Some sources make special issue of the nature of a group when its underlying set is a subset of, or derived directly from, numbers themselves.

In such treatments, a group whose operation is addition is then referred to as an additive group.

On $\mathsf{Pr} \infty \mathsf{fWiki}$ we consider all groups, whatever their nature, to be instances of the same abstract concept, and therefore make no such distinction.

Also denoted as

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

Also see