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.
This property has the following metaproperties
- passes to $eRe$ for any idempotent $e$
- passes to $eRe$ for any full idempotent $e$
- passes to matrix rings
- Morita invariant