Note on the ring of integers of a Kummer extension of prime degree. II

Abstract

Let $p$ be a prime number, and $a$ $(\in \mathbf{Q}^{\times})$ a rational number. Then, F. Kawamoto proved that the cyclic extension $\mathbf{Q}(\zeta_p, a^{1/p})/\mathbf{Q}(\zeta_p)$ has a normal integral basis if it is at most tamely ramified. We give some generalized version of this result replacing the base field $\mathbf{Q}$ with some real abelian fields of prime power conductor.