# Definition:Ring (Abstract Algebra)/Ring Less Zero

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## Definition

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:

- $R_{\ne 0} = R \setminus \set 0$

## Also denoted as

Most sources use $R^*$.

However, this is also uses by some sources to mean the group of units of a ring $R$.

## Sources

- 1965: Seth Warner:
*Modern Algebra*... (previous) ... (next): $\S 21$