Quotient Ring of Integers and Zero

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

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

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