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Note on the ring of integers of a Kummer extension of prime degree. V. (English) Zbl 1106.11308

Summary: Let \(\ell\) be a prime number, and \(K\) a number field with \(\zeta_{\ell} \in K^{\times}\). We give a simple necessary and sufficient condition for all tame Kummer extensions over \(K\) of degree \(\ell\) to have a relative normal integral basis. The result is given in terms of the class number and the group of units of \(K\).
Parts I–IV, cf. Comment. Math. Univ. St. Pauli 52, No. 1, 59–67 (2003; Zbl 1058.11063), Proc. Japan Acad., Ser. A 77, No. 1, 25–28 (2001; Zbl 0989.11062), 77, No. 5, 71–73 (2001; Zbl 0989.11063), 77, No. 6, 92–94 (2001; Zbl 0998.11065)

MSC:

11R04 Algebraic numbers; rings of algebraic integers
11R29 Class numbers, class groups, discriminants
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References:

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