Definition:Additive Notation

{{WIP|Merge this with the similar subsection in [{Definition:Abelian Group]].}}

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 $\left({S, +}\right)$ 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.

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

Also see

 * Multiplicative notation