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