# Property detail

Property name: exchange
Definition: If $a+b=1$, there exists $r$ and $s$ such that $ar$ and $bs$ are idempotents and $ar+bs=1$
Rings with property: 47
Rings without property: 16

## Metaproperties

This property has the following metaproperties
• Passes to eRe for any idempotent e (theorem needed)
• Passes to eRe for any full idempotent e (theorem needed)