Lesson plan
Additive map
In algebra, an additive map or additive function is a function f that preserves the addition operation: f(x + y) = f(x) + f(y) for every pair of elements x and y in the domain of . For example, any linear map is additive. When the domain is the integers (ℤ), this is called a \Z -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. More formally, an additive map is a \Z -module homomorphism. Since an abelian group is a \Z -module, it may be defined as a group homomorphism between abelian groups. A map V \times W \to X that is additive in each of two arguments separately is called a bi-additive map or a \Z -bilinear map.
Article summary
In algebra, an additive map or additive function is a function f that preserves the addition operation: f(x + y) = f(x) + f(y) for every pair of elements x and y in the domain of . For example, any linear map is additive. When the domain is the integers (ℤ), this is called a \Z -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. More formally, an additive map is a \Z -module homomorphism. Since an abelian group is a \Z -module, it may be defined as a group homomorphism between abelian groups. A map V \times W \to X that is additive in each of two arguments separately is called a bi-additive map or a \Z -bilinear map.
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- Summarise the article in your own words. Which single claim would you verify first, and why?
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