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!!