Definition:Multiplicative Notation

Definition
Multiplicative notation, also called product notation, is a convention for representing a binary operation of an algebraic structure.

Let $$S$$ 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 $$y$$. There is no symbol used to define the operation itself.


 * $$e$$ or $$1$$ is used for the identity element.


 * $$x^{-1}$$ is used for the inverse element.


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

This notation is usual in group theory when discussing the general group.

It is also usual in ring theory for the ring product.

Also see

 * Additive notation