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Cyclic extensions of degree \(\ell\) over an \(\ell\)-regular number field. (Erratum à l’article: Extensions cycliques de degré \(\ell\) de corps de nombres \(\ell\)-réguliers.) (French) Zbl 0872.11050

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.
Reviewer: V.Ennola (Turku)

MSC:

11R70 \(K\)-theory of global fields
11R18 Cyclotomic extensions
11R20 Other abelian and metabelian extensions

Citations:

Zbl 0834.11049
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References:

[1] Soriano, F., Extensions cycliques de degré de corps de nombres -réguliers, J. Théor. Nombres Bordeaux4 (1994), 407-420. · Zbl 0834.11049
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