# Property detail

Property name: connected

Definition: The only idempotents are 0 and 1

Rings with property: 41

Rings without property: 17

## 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)
- passes to subrings
(theorem needed)

This property does not have the following metaproperties

- passes to quotient rings
(counterexample needed)
- passes to matrix rings
(counterexample needed)
- Morita invariant
(counterexample needed)
- stable under finite products
(counterexample needed)
- stable under products
(counterexample needed)