By an integral domain, we mean here, a ring (not necessarily with unity) in which $ab=0$ implies $a=0$ or $b=0$.
Question: If an integral domain without unity has positive characteristic, is it necessarily prime?
An integral domain $D$ is said to be of finite characteristic if there exists a positive integer $m$ such that $ma=0$ for all $a\in D$. [cf. Topics in Algebra- I. N. Herstein, 2nd Ed., p. 129]
My question is a slight modification of Problem 6 in [Topics in Algebra- I. N. Herstein, 2nd Ed., p. 130]