Additive group

Anadditive groupis agroupof which the group operation is to be thought of asadditionin some sense. It is usuallyabelian,and typically written using the symbol+for its binary operation.

This terminology is widely used with structures equipped with several operations for specifying the structure obtained by forgetting the other operations. Examples include theadditive groupof theintegers,of avector spaceand of aring.This is particularly useful with rings andfieldsto distinguish the additive underlying group from themultiplicative groupof theinvertible elements.

In older terminology, an additive subgroup of a ring has also been known as amodulormodule(not to be confused with amodule).