# Characteristic of a ring

From Maths

## Definition

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*

## References

- ↑ Fundamentals of Abstract Algebra - Neal H. McCoy