Let $K/F$ be a Kummer cyclic extension of number fields. In the case when the degree is a prime number, G\'omez Ayala gave an explicit criterion for the existence of a normal integral basis. More recently Ichimura proposed a generalization of that result for cyclic extensions of arbitrary degree, but we have found that Ichimura's result is incorrect. In this paper we present a counter-example to Ichimura's result as well as the correct generalization of G\'omez Ayala's result.
Normal integral bases for cyclic Kummer extensions
DEL CORSO, ILARIA;
2010-01-01
Abstract
Let $K/F$ be a Kummer cyclic extension of number fields. In the case when the degree is a prime number, G\'omez Ayala gave an explicit criterion for the existence of a normal integral basis. More recently Ichimura proposed a generalization of that result for cyclic extensions of arbitrary degree, but we have found that Ichimura's result is incorrect. In this paper we present a counter-example to Ichimura's result as well as the correct generalization of G\'omez Ayala's result.File in questo prodotto:
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