\begin{definition}[Definition:Division Product]
Let $\struct {R, +, \circ}$ be a commutative ring with unity.
Let $\struct {U_R, \circ}$ be the group of units of $\struct {R, +, \circ}$.
Then we define the following notation:
:$\forall x \in U_R, y \in R$, we have:
::$\dfrac y x := y \circ \paren {x^{-1} } = \paren {x^{-1} } \circ y$
$\dfrac y x$ is a '''division product''', and $\dfrac y x$ is voiced '''$y$ divided by $x$'''.
We also write (out of space considerations) $y / x$ for $\dfrac y x$.
This notation is usually used when $\struct {R, +, \circ}$ is a field.
\end{definition}