Property: countable

Definition: The underlying set of the ring is countable.

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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