Ring of Integers Modulo Prime is Integral Domain/Proof 1
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Corollary to Ring of Integers Modulo Prime is Field
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 an integral domain.
Proof
We have that a Field is Integral Domain.
We also have that a Finite Integral Domain is Galois Field.
The result follows from Ring of Integers Modulo Prime is Field.
$\blacksquare$