Additive map

In algebra an additive map, Z-linear map or additive function is a function that preserves the addition operation:

for any two elements x and y in the domain. For example, any linear map is additive. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial. Any homomorphism f between abelian groups is additive by this definition.