# 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: 51
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)