# Property: commutative

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