additive map

Z-module homomorphism

EntityQ22963169

Also known as additive function · Z-linear map

Subclass of: homomorphism

Overview

From Wikipedia, the free encyclopedia · Read full article · Text CC BY-SA 4.0

In algebra, an additive map or additive function is a function that preserves the addition operation: for every pair of elements and in the domain of ⁠⁠. For example, any linear map is additive. When the domain is the integers (ℤ), this is called a -linear map. When the domain is the real numbers, this is Cauchy's functional equation. For a specific case of this definition, see additive polynomial.

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Different from: additive function
Defining formula: f(x + y) = f(x) + f(y)
Has characteristic: additivity
In defining formula: f symbol represents: function
x symbol represents: argument of a function
y symbol represents: argument of a function

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Freebase ID/m/0131vj6r

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Source last edited September 14, 2026. AIDb refreshes this page daily.

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AIDb. (2026). additive map (Q22963169). Retrieved from https://aidb.si/e/additive-map-Q22963169