Characteristic of Ring of Integers Modulo Prime

Theorem
Let $\left({\Z_p, +, \times}\right)$ be the ring of integers modulo $p$, where $p$ is a prime number.

The characteristic of $\left({\Z_p, +, \times}\right)$ is $p$.

Proof
From Ring of Integers Modulo Prime is Field we have that $\left({\Z_p, +, \times}\right)$ is a field.

So Characteristic of Ring with No Zero Divisors applies, and so the characteristic of $\left({\Z_p, +, \times}\right)$ is prime.

The result follows.