Property: periodic

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

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Metaproperties:

This property has the following metaproperties
  • 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
This property does not have the following metaproperties
  • passes to matrix rings (counterexample)
  • Morita invariant (counterexample)
  • passes to polynomial rings (counterexample needed)
  • passes to power series ring (counterexample needed)