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Chatelain’s integer bases for biquadratic fields

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Abstract

Let \(K=\mathbb {Q}(\sqrt{dm}, \sqrt{dn})\) be a biquadratic field. In this paper we give a new integral basis for \(\mathbb {Z}_{K}\), by applying to biquadratic fields a method of D. Chatelain, for building formel integral bases of n-quadratic fields’ ring of integers. We give some examples. We set the monogenesis problem’s equations, and find the same characterizations that we’ve found, when we had used other bases. We give also new expressions for the elements of monogenesis.

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  1. Laboratoire de Mathématiques Fondamentales, UFR de Mathématiques et Informatique, Université Félix Houphouet Boigny, 22 BP 582, Abidjan 22, Côte d’Ivoire

    François E. Tanoé

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  1. François E. Tanoé
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Correspondence to François E. Tanoé.

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Tanoé, F.E. Chatelain’s integer bases for biquadratic fields. Afr. Mat. 28, 727–744 (2017). https://doi.org/10.1007/s13370-016-0476-2

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