Property: 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.

Metaproperties

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