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An additive category is a category for which the morphism sets have the structure of Abelian groups. It satisfies some, but not all the properties of an Abelian category.

An additive cellular automaton is a cellular automaton whose rule is compatible with an addition of states. Typically, this addition is derived from modular arithmetic. ...

An additive function is an arithmetic function such that whenever positive integers a and b are relatively prime, f(ab)=f(a)+f(b). An example of an additive function is ...

An additive group is a group where the operation is called addition and is denoted +. In an additive group, the identity element is called zero, and the inverse of the ...

The identity element of an additive group G, usually denoted 0. In the additive group of vectors, the additive identity is the zero vector 0, in the additive group of ...

In an additive group G, the additive inverse of an element a is the element a^' such that a+a^'=a^'+a=0, where 0 is the additive identity of G. Usually, the additive inverse ...

The portion of number theory concerned with expressing an integer as a sum of integers from some given set.

Consider the process of taking a number, adding its digits, then adding the digits of the number derived from it, etc., until the remaining number has only one digit. The ...

Let k be a field of finite characteristic p. Then a polynomial P(x) in k[x] is said to be additive iff P(a)+P(b)=P(a+b) for {a,b,a+b} subset k. For example, P(x)=x^2+x+4 is ...

A mathematical object S is said to be additively closed if a,b in S implies that a+b in S.