Definition:Additive Notation

Definition
Additive notation is a convention often used for representing a commutative binary operation of an algebraic structure.

The symbol used for the operation is $+$.

Let $\struct {S, +}$ be such an algebraic structure, and let $x, y \in S$.
 * $x + y$ is used to indicate the result of the operation $+$ on $x$ and $y$.


 * $e$ or $0$ is used for the identity element. Note that in this context, $0$ is not a zero element.


 * $-x$ is used for the inverse element.


 * $n x$ is used to indicate the $n$th power of $x$.

This notation is usual in group theory when discussing a general abelian group.

It is also usual in:
 * ring theory for the ring addition operator
 * field theory for the field addition operator.

In this context, the inverse of an element $x$ is often referred to as the negative of $x$.

Also see

 * Definition:Multiplicative Notation