# Definition:Additive Notation

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## 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 $x$.