Canonical_Epimorphism_from_Integers_by_Principal_Ideal

Let $m$ be a strictly positive integer. Let $\left({m}\right)$ be the principal ideal of $\Z$ generated by $m$. The restriction to $\N_m$ of the canonical epimorphism $q_m$ from the ring $\left({\Z, +, \times}\right)$ onto $\left({\Z, +, \times}\right) / \left({m}\right)$ is an isomorphism from the ring $\left({\N_m, +_m, \times_m}\right)$ of integers modulo $m$ onto the quotient ring $\left({\Z, +, \times}\right) / \left({m}\right)$. In particular, $\left({\Z, +, \times}\right) / \left({m}\right)$ has $m$ elements.