## Resources for learning about this property:

- N. Jacobson. Basic algebra I. (2012) @ Section 8.5

## Metaproperties:

This property has the following metaproperties

- passes to $eRe$ for any full idempotent $e$
- passes to $eRe$ for any idempotent $e$
- passes to localizations
- passes to quotient rings
- passes to subrings
- passes to the center
- stable under finite products
- stable under products

This property

**does not** have the following metaproperties

- Morita invariant
(counterexample needed)
- passes to matrix rings
(counterexample needed)
- passes to polynomial rings
(counterexample needed)
- passes to power series ring
(counterexample needed)