# Property detail

Property name: $I_0$

Definition: Every right ideal not contained in $rad(R)$ contains a nonzero idempotent. Also called "semipotent".

Rings with property: 47

Rings without property: 15

## 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)