# 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)