The number 0 is the "additive identity" for integers, real numbers, and complex numbers.

The ring in which e is equal to the additive identity must have only one element.

The additive identity familiar from elementary mathematics is zero, denoted 0.

A ring or field is a group under the operation of addition and thus these also have a unique additive identity 0.

In the quaternions, 0 is the additive identity.

The two elements are nearly always called 0 and 1, being the additive and multiplicative identities, respectively.

The zero matrix is the additive identity in .

An additive identity is the identity element in an additive group.

Many absorbing elements are also additive identities, including the empty set and the zero function.

Some authors prefer to replace addition with minimization; then the additive identity is positive infinity.