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A cyclotomic field is a number field obtained by adjoining a complex primitive root of unity to $\mathbb Q$, the field of rational numbers.

7 votes

Trace of n-th root of unity in cyclotomic extension of p-adic rationals

You're asking for the trace down to $\mathbf Q_p$ of any $n$th root of unity $\xi_n$ in a cyclotomic extension of $\mathbf Q_p$. David has interpreted the question in his answer to be the case $\xi_n …
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16 votes

Quick proof of the fact that the ring of integers of $\mathbb Q(\zeta_n)$ is $\mathbb Z[\zet...

The ring of integers $R_n$ of ${\mathbf Q}(\zeta_n)$ contains ${\mathbf Z}[\zeta_n]$ as a subring with finite index. To show the containment of rings is an equality, it suffices to show the inclusion …
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