\begin{definition}[Definition:Ring (Abstract Algebra)/Ring Less Zero]
Let $\struct {R, *, \circ}$ be a ring.
It is convenient to have a symbol for $R \setminus \set 0$, that is, the set of all elements of the ring without the zero. Thus we usually use:
:$R_{\ne 0} = R \setminus \set 0$
\end{definition}