Definition:Division Product

Let $$\left({R, +, \circ}\right)$$ be a commutative ring with unity.

Let $$\left({U_R, \circ}\right)$$ be the group of units of $$\left({R, +, \circ}\right)$$.

Then we define the following notation:

$$\forall x \in U_R, y \in R$$, we have:

$$\frac y x = y \circ \left({x^{-1}}\right) = \left({x^{-1}}\right) \circ y$$

This is referred to as $$y$$ divided by $$x$$.

We also write (out of space considerations) $$y / x$$ for $$\frac y x$$.