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.
Citation
Humio Ichimura. "Note on the ring of integers of a Kummer extension of prime degree. II." Proc. Japan Acad. Ser. A Math. Sci. 77 (2) 25 - 28, Feb. 2001. https://doi.org/10.3792/pjaa.77.25
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