Abstract
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 $K$.
Citation
Humio Ichimura. "Note on the ring of integers of a Kummer extension of prime degree. V." Proc. Japan Acad. Ser. A Math. Sci. 78 (6) 76 - 79, June 2002. https://doi.org/10.3792/pjaa.78.76
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