Look up **additive group** in Wiktionary, the free dictionary.

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 for specifying the structure obtained by forgetting the other operations. Examples include the *additive group*^{[1]} 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]}

**^**Bourbaki, N. (1998) [1970], "§8.1 Rings",*Algebra I: Chapters 1–3*, Springer, p. 97, ISBN 978-3-540-64243-5**^**"MathOverflow: The Origin(s) of Modular and Moduli". Retrieved 8 March 2024.