Ring of Integers Modulo Prime is Integral Domain

Corollary to Ring of Integers Modulo Prime is Field
Let $m \in \Z: m \ge 2$.

Let $\left({\Z_m, +, \times}\right)$‎ be the ring of integers modulo $m$.

Then:
 * $m$ is prime

iff:
 * $\left({\Z_m, +, \times}\right)$ is an integral domain.

Proof
We have that a field is an integral domain.

We also have that a finite integral domain is a field.

The result follows from Ring of Integers Modulo Prime is Field.