Dedekind’s criterion and monogenesis of number fields

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]]....

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Bibliographic Details
Main Authors: El Fadil, Lhoussain, Benyakkou, Hamid
Format: Conference Proceeding
Language:English
Subjects:
Criteria
Integers
Polynomials
Online Access:Get full text
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Summary: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.
ISSN:0094-243X
1551-7616
DOI:10.1063/1.5090631