On the ring of integers of a tame Kummer extension over a number field. (Q1420635)

Let \(K/F\) be a finite Galois extension of number fields. Generalizing results of \textit{E. J. Gómez Ayala} [J. Théor. Nombres Bordx. 6, 95--116 (1994; Zbl 0822.11076)], the author characterizes tamely ramified cyclic Kummer extensions \(K/F\) with normal integral bases. As an application, he obtains the following capitulation result: given an integer \(m \geq 2\) and a number field \(F\) containing the \(m\)th roots of unity, there is a finite extension \(L/F\) such that for any abelian extension \(K/F\) with exponent \(m\), the extension \(LK/L\) has a normal integral basis.