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If $K$ is a number field with ring of integers $\mathcal{O}_K$, then for all $\alpha\in\mathcal{O}_K$ such that $K=\Q(\alpha)$, the index of $\alpha$, $i(\alpha)$ is the index of the order $\Z[\alpha]$.

The index of the number field is the greatest common divisor of all $i(\alpha)$ with $\alpha$ as above.

Knowl status:
  • Review status: beta
  • Last edited by John Jones on 2022-02-24 13:13:32
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