Nonunit (source code)
= Nonunit
A <nonunit> is an element of a <ring> with no two-sided <multiplicative inverse> in that <ring>. For example, $2$ is a <nonunit> in the <integers>, even though multiplication by $2$ obeys the <cancellation law>. Thus being a <nonunit> does not imply being a <zero divisor>.
The <set> of <nonunits> need not be an <ideal>. In $\mathbb Z$, both $2$ and $-3$ are <nonunits>, but their <sum> $-1$ is a <unit>. In a <commutative> <local ring>, by contrast, the <nonunits> form its unique <maximal ideal>.
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