Is it possible for a finite ring with unity in the form of $\Bbb Z / p$ where $p$ is not prime to be a PID?
2026-02-23 13:47:47.1771854467
Is $\Bbb Z / p$ where $p$ is not prime a PID?
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$\mathbb Z/n\mathbb Z$ is always a principal ideal ring, because it is a homomorphic image of the principal ideal ring $\mathbb Z$.
It is never a principal ideal domain when $n$ is composite, however, because a nontrivial factorization of $n$ leads directly to zero divisors in the ring.