Definition:Ring (Abstract Algebra)/Ring Less Zero

Definition
Let $\struct {R, *, \circ}$ be a ring whose zero is $0$. 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:
 * $R_{\ne 0} = R \setminus \set 0$