Exercise 1, § 1

Let $A$ be a not necessarily commutative ring, not zero and without divisors of zero (I, p. 98). Show that if there exists an integer $m \geq 1$ such that $mA = 0$, then the set of all integers having this property is an ideal $p\mathbf{Z}$, where $p$ is a prime number, and $A$ is a ring of characteristic $p$.