\begin{definition}[Definition:Additive Notation]
'''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 $x$.
\end{definition}