\begin{definition}[Definition:Multiplicative Notation]
'''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 the usual notation in:
:ring theory for the ring product
:field theory for the field product.
\end{definition}