Additive functions

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Not to be confused with additive arithmetic functions, a term with a different meaning used in number theory.

In algebra, an additive function (or additive map) is a function that preserves the addition operation, i.e.

$f(x+y)=f(x)+f(y),$

for any two elements $x$ and $y$ in the domain. For example, any linear map is additive.

See also

• Multiplicative functions