# Property detail

Property name: unit regular

Definition: For every $x$, there exists a unit $u$ such that $x=xux$

Rings with property: 14

Rings without property: 65

## Metaproperties

This property has the following metaproperties

- passes to quotient rings
(theorem needed)
- stable under products
(theorem needed)
- stable under finite products
(theorem needed)
- Morita invariant
(theorem needed)