# A note ON MONOGENEITY of pure number fields

@inproceedings{Fadil2021ANO, title={A note ON MONOGENEITY of pure number fields}, author={Lhoussain El Fadil}, year={2021} }

Gassert’s paper ”A NOTE ON THE MONOGENEITY OF POWER MAPS” is cited at least by 17 papers in the context of monogeneity of pure number fields despite some errors that it contains and remarks on it. In this note, we point out some of these errors, and make some improvements on it.

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## References

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It is proved that if m is a square-free rational integer, m ≡ 1(mod 4) and m≢ ± 1( mod 9), then the pure sextic field L = Q(m6) is not monogenic.

A NOTE ON THE MONOGENEITY OF POWER MAPS

Let φ(x) = xd − t ∈ Z[x] be an irreducible polynomial of degree d ≥ 2, and let θ be a root of φ. The purpose of this paper is to establish necessary and sufficient conditions for φ(x) to be…

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