Additive group

An additive group is a group of which the group operation is to be thought of as addition in some sense. It is usually abelian, and typically written using the symbol + for its binary operation.

This terminology is widely used with structures equipped with several operations to specify structures obtained by forgetting the other operations. Examples include the additive group¹ of the integers, of a vector space and of a ring. This is particularly useful with rings and fields to distinguish the additive underlying group from the multiplicative group of the invertible elements.

In older terminology, an additive subgroup of a ring has also been known as a modul or module (not to be confused with a module).²