Quotient Ring of Integers and Zero

Theorem
Let $\struct {\Z, +, \times}$ be the integral domain of integers.

Let $\ideal 0$ be the principal ideal of $\struct {\Z, +, \times}$ generated by $0$.

The quotient ring $\struct {\Z / \ideal 0, +, \times}$ is isomorphic to $\struct {\Z, +, \times}$.