Abstract
Let l be an odd prime number and k=Q(ζ+ζ−1) where ζ is a primitive l-th root of unity. We provide a sufficient condition for the monogenity of a cyclic extension Ks/k of degree l, where s is an integer of k and Ks is a field defined by Rikuna's generic cyclic polynomial. As an application, we prove that there exist infinitely many monogenic extensions Ks/k for l≥5.
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