Additive identity

In mathematics, the additive identity of a set that is equipped with the operation of addition is an element which, when added to any element x in the set, yields x. One of the most familiar additive identities is the number 0 from elementary mathematics, but additive identities occur in other mathematical structures where addition is defined, such as in groups and rings.

Contents
1 Elementary examples
2 Formal definition
3 Further examples
4 Properties
4.1 The additive identity is unique in a group
4.2 The additive identity annihilates ring elements
4.3 The additive and multiplicative identities are different in a non-trivial ring
5 See also