Property: countable

Definition: The underlying set of the ring is countable.

Metaproperties

This property has the following metaproperties
  • passes to $eRe$ for any full idempotent $e$
  • passes to $eRe$ for any idempotent $e$
  • passes to subrings
  • passes to the center
  • stable under finite products
  • passes to matrix rings
  • Morita invariant
  • passes to localizations
  • passes to polynomial rings
  • passes to quotient rings
This property does not have the following metaproperties