Definition: No nonzero nilpotent elements

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- 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

- Morita invariant (counterexample)
- passes to matrix rings (counterexample)
- passes to quotient rings (counterexample)