Additive group

Short description: Group with an addition as its operation

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]

## References

1. ↑ Bourbaki, N. (1998), "§8.1 Rings", Algebra I: Chapters 1–3, Springer, p. 97, ISBN 978-3-540-64243-5, https://books.google.com/books?id=STS9aZ6F204C&pg=PA97
2. ↑ "MathOverflow: The Origin(s) of Modular and Moduli". https://mathoverflow.net/questions/300013/the-origins-of-modular-and-moduli/300076#300076.

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