= Characteristic of a rng
{title2=$\operatorname{char}R=\min\{n>0:nr=0\text{ for all }r\in R\}$}
The <characteristic of a rng> is the least positive <integer> annihilating every element of its additive <abelian group>, or zero if no such integer exists. In a unital <ring> this equals the <characteristic of a ring>: $n1=0$ implies $nr=(n1)r=0$, and annihilating every element in particular annihilates $1$. In a finite rng it is the <exponent of a finite group> of the additive group.
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