# Property detail

Property name: weakly clean
Definition: For all $a\in R$, there exists a unit $u$ and idempotent $e$ such that $a-e-u\in (1-e)Ra$. This is left-right symmetric.
Rings with property: 48
Rings without property: 0

## Metaproperties

This property has the following metaproperties
• Morita invariant (theorem needed)
• passes to matrix rings (theorem needed)
• Passes to eRe for any idempotent e (theorem needed)
• Passes to eRe for any full idempotent e (theorem needed)