# Property detail

Property name: clean

Definition: Every element is the sum of a unit and an idempotent

Rings with property: 48

Rings without property: 18

## Metaproperties

This property has the following metaproperties

- passes to matrix rings
(theorem needed)
- stable under finite products
(theorem needed)
- stable under products
(theorem needed)

This property does not have the following metaproperties

- passes to quotient rings
(counterexample needed)
- Passes to eRe for any idempotent e
(counterexample needed)
- Morita invariant
(counterexample needed)