Characteristic of a ring

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Let [ilmath]R[/ilmath] be a ring. The characteristic of a ring is defined as follows[1]:

  • If [ilmath]\exists n\in\mathbb{N}_{\ge 0} [/ilmath] such that [ilmath]\forall a\in R[/ilmath] we have [ilmath]na=0[/ilmath] then the smallest such integer [ilmath]n[/ilmath] is the characteristic of [ilmath]R[/ilmath]
  • If [ilmath]\nexists[/ilmath] such an [ilmath]n[/ilmath] we say [ilmath]R[/ilmath] has characteristic 0


  1. Fundamentals of Abstract Algebra - Neal H. McCoy