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I cannot find a good reference for the proof that the ring of integers in a cyclotomic field $\mathbb{Q}(\zeta_n)$ is $\mathbb{Z}[\zeta_n]$. The proof I usually find does an induction on the number of prime factors of $n$, coupled with a lenghty lengthy and somewhat computational proof in the case where $n$ is the power of a prime.

Do you know a quicker and possibly more conceptual approach?

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# Quick proof of the fact that the ring of integers of $\mathbb{Q}(\zeta_n)$Q(\zeta_n) is $\mathbb{Z}[\zeta_n]$?Z[\zeta_n]?

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# Quick proof of the fact that the ring of integers of Q(\zeta_n)$\mathbb{Q}(\zeta_n)$ is Z[\zeta_n]?$\mathbb{Z}[\zeta_n]$?

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