If $R$ is a P.I.D. and $p\in R$ is prime, is it the case that $R/<p^k>$ will be a P.I.D for all k? If so how would one show this?
2026-03-30 17:15:52.1774890952
quotient of P.I.D by a prime power a P.I.D?
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No. If $k\ge 2$, then the quotient will have zero divisors and not even be an integral domain. (A PID needs to be an integral domain by definition).