# 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