Characteristic of a ring
= Characteristic of a ring
{title2=$\operatorname{char}R$}
= Ring characteristic
{synonym}
The characteristic of a <ring> $R$ is the least positive <integer> $n$ satisfying $n\cdot1_R=0$, or zero if no such <integer> exists. A nonzero <ring> of positive characteristic has prime characteristic when it is an <integral domain>.