Newton polygons and p-integral bases of quartic number fields

Lhoussain El Fadil; Jesús Montes; Enric Nart

doi:10.1142/S0219498812500739

Newton polygons and p-integral bases of quartic number fields

Lhoussain El Fadil, Jesús Montes, Enric Nart

Department of Mathematics

Research output: Contribution to journal › Article › Research › peer-review

9 Citations (Scopus)

Abstract

Let p be a prime number. In this paper we use an old technique of Ø. Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by p-regular equations. To illustrate the potential applications of this construction, we derive from this result an explicit description of a p-integral basis of an arbitrary quartic field in terms of a defining equation. © 2012 World Scientific Publishing Company.

Original language	English
Article number	1250073
Journal	Journal of Algebra and Its Applications
Volume	11
Issue number	4
DOIs	https://doi.org/10.1142/S0219498812500739
Publication status	Published - 1 Aug 2012

Keywords

Newton polygon
p-integral basis
quartic field

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AU - Nart, Enric

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N2 - Let p be a prime number. In this paper we use an old technique of Ø. Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by p-regular equations. To illustrate the potential applications of this construction, we derive from this result an explicit description of a p-integral basis of an arbitrary quartic field in terms of a defining equation. © 2012 World Scientific Publishing Company.

AB - Let p be a prime number. In this paper we use an old technique of Ø. Ore, based on Newton polygons, to construct in an efficient way p-integral bases of number fields defined by p-regular equations. To illustrate the potential applications of this construction, we derive from this result an explicit description of a p-integral basis of an arbitrary quartic field in terms of a defining equation. © 2012 World Scientific Publishing Company.

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KW - quartic field

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DO - 10.1142/S0219498812500739

M3 - Article

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JO - Journal of Algebra and Its Applications

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