Let $K$ be an arbitrary algebraic number field. We know that the fraction field of $\mathcal{O}_K$ is $K$ which is always isomorphic to some $\mathbb{Z}[x]/(f(x))$. $\mathcal{O}_K$ also has dimension one so I was wondering if something similar might be said of $\mathcal{O}_K/m$, for any non-zero prime(=maximal) ideal of $\mathcal{O}_K$? Is it isomorphic to some quotient of $\mathbb{Z}[x]$?
2026-04-02 21:19:53.1775164793
Quotient ring of the ring of integers of an algebraic number field and its fraction field
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