# Property: reduced

Definition: No nonzero nilpotent elements

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## Metaproperties:

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