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Let $K$ be abelian over $\mathbb Q$, $E_K$ its unit group, $\mathbb Q(\zeta_n)$ be a minimal cyclotomic field containing $K$ and $C$ its cyclotomic units.

By the definition, we know that the group of cyclotomic units of $K$ is defined by $C_K:= C\cap E_K$.

I am wondering if there is a definition when $\mathbb Q(\zeta_n)$ is not a minimal field containing $K$.

Thanks!!

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    $\begingroup$ I cannot make any sense of this question. What exactly are you trying to ask? $\endgroup$ May 8, 2014 at 18:37
  • $\begingroup$ In my opinion, I think he/she want to ask if we can replace the "minimal" sense of cyclotomic field with a larger cyclotomic field containing K. Maybe, he/she think it holds too. $\endgroup$
    – user50579
    May 8, 2014 at 20:31
  • $\begingroup$ @mike - this is my reading too (and Olivier's as well as I see from the edit). Nevertheless a clarification would be welcome; could the submitter please edit the question? $\endgroup$
    – GNiklasch
    May 9, 2014 at 12:44

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