Quotient Ring of Integers with Principal Ideal

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

Let $n \in \Z$.

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

The quotient ring $\left({\Z, +, \times}\right) / \left({n}\right)$ is isomorphic to $\left({\Z_n, +_n, \times_n}\right)$, the ring of integers modulo n.

Note the special cases where $n = 0$ or $1$:


 * Quotient Ring of Integers and Zero


 * Quotient Ring of Integers and Principal Ideal from Unity