Additive group

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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.


  1. Bourbaki, N. (1998), "§8.1 Rings", Algebra I: Chapters 1–3, Springer, p. 97, ISBN 978-3-540-64243-5,