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]}
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Subgroups of Group of Integers with Addition

Additive Identity

Additive Identity
Transcription
References
 ^ Bourbaki, N. (1998) [1970], "§8.1 Rings", Algebra I: Chapters 1–3, Springer, p. 97, ISBN 9783540642435
 ^ "MathOverflow: The Origin(s) of Modular and Moduli". Retrieved 8 March 2024.