Quotient Ring of Integers and Zero

Theorem
Let $\left({\Z, +, \times}\right)$ be the integral domain of integers.

Let $\left({0}\right)$ be the principal ideal of $\left({\Z, +, \times}\right)$ generated by $0$.

The quotient ring $\left({\Z / \left({0}\right), +, \times}\right)$ is isomorphic to $\left({\Z, +, \times}\right)$.