Definition: For every element $x\in R$, there exists a natural number $n_x> 1$ such that $x^{n_x}=x$.

(No citations retrieved.)

- passes to subrings
- passes to the center
- passes to $eRe$ for any full idempotent $e$
- passes to $eRe$ for any idempotent $e$
- passes to quotient rings

- passes to matrix rings (counterexample)
- Morita invariant (counterexample)
- passes to polynomial rings (counterexample needed)
- passes to power series ring (counterexample needed)