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2019•AIP conference proceedingsRequires access

Dedekind’s criterion and monogenesis of number fields

Lhoussain El Fadil, Hamid Ben Yakkou

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Abstract

Let L = ℚ(α) be a number field and ℤL its ring of integers, where α is a complex root of a monic irreducible polynomial F(X) ∈ ℤ[X]. In this paper, we give a new efficient version of Dedekind’s criterion, i.e., an efficient criterion to test either p divides or does not divide the index [ℤL: ℤ[α]]. As application, we study the integral closedness of ℤ[α] and the monogenity of a familly of octic number fields.

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What this paper is about

Let L = ℚ(α) be a number field and ℤL its ring of integers, where α is a complex root of a monic irreducible polynomial F(X) ∈ ℤ[X]. In this paper, we give a new efficient version of Dedekind’s criterion, i.e., an efficient criterion to test either p divides or does not divide the index [ℤL: ℤ[α]]. As application, we study the integral closedness of ℤ[α] and the monogenity of a familly of octic number fields.

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Available abstract

Let L = ℚ(α) be a number field and ℤL its ring of integers, where α is a complex root of a monic irreducible polynomial F(X) ∈ ℤ[X]. In this paper, we give a new efficient version of Dedekind’s criterion, i.e., an efficient criterion to test either p divides or does not divide the index [ℤL: ℤ[α]]. As application, we study the integral closedness of ℤ[α] and the monogenity of a familly of octic number fields.

Key concepts: Monic polynomial, Dedekind cut, Algebraic number field, Mathematics, Irreducible polynomial, Field (mathematics), Polynomial ring, Ring of integers

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