Ring of Integers Modulo Prime is Field

Theorem
Let $m \in \Z: m \ge 2$.

Let $\struct {\Z_m, +, \times}$‎ be the ring of integers modulo $m$.

Then:
 * $m$ is prime


 * $\struct {\Z_m, +, \times}$ is a field.
 * $\struct {\Z_m, +, \times}$ is a field.

Also see

 * Definition:Field of Integers Modulo Prime


 * Definition:Galois Field