# 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.

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## 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