Definition: $xy=yx$ for all $x$ and $y$ in the ring

## Metaproperties

This property has the following metaproperties

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

This property

**does not** have the following metaproperties