# Property detail

Property name: commutative

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

Rings with property: 40

Rings without property: 39

## Metaproperties

This property has the following metaproperties

- passes to subrings
(theorem needed)
- stable under finite products
(theorem needed)
- stable under products
(theorem needed)
- Passes to eRe for any idempotent e
(theorem needed)
- Passes to eRe for any full idempotent e
(theorem needed)
- passes to quotient rings
(theorem needed)
- passes to localizations
(theorem needed)

This property does not have the following metaproperties

- Morita invariant
(counterexample needed)
- passes to matrix rings
(counterexample needed)