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

Also see

 * Multiplicative notation