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

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