In my book (Herstein) this is a statement:
An integral domain $D$ is said to be of finite characteristic if there exists a positive integer $m$ such that $ma=0$ for all $a$ in $D$.
But by definition an integral domain can't have zero-divisors right? So how can an integral domain have finite characteristic because isn't the characteristic a zero-divisor for every a in D? Is it that m can't be in D? I'm confused, if anyone could clarify this for me I'd really appreciate it.