Cyclic extensions of degree \(\ell\) over an \(\ell\)-regular number field (Q5894670)

Let \(\ell\) be an odd prime and let \(L/K\) be a cyclic extension of degree \(\ell\) of \(\ell\)-regular number fields containing the \(\ell\)th roots of unity. An erroneous formula for the unit index \((E_K: E_K\cap N_{L/K})\) in the article in question [ibid. 6, 407-420 (1994; Zbl 0834.11049)] is corrected. The complete list of all such extensions \(L/K\) has to be slightly modified, correspondingly. A numerical example is rectified and completed.