On power integral bases of certain pure number fields defined by $$x^{42} - m$$

Let K = ℚ(α) be a number field generated by a complex root a of a monic irreducible polynomial ƒ (x) = x36 − m, with m ≠ ±1 a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≠ ±1 (mod 9) then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡±1 (mod 9), then the number field K is not monogenic.

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On power integral bases for certain pure number fields defined by x24 – m

Studia Scientiarum Mathematicarum Hungarica ◽

10.1556/012.2020.57.3.1472 ◽

2020 ◽

Vol 57 (3) ◽

pp. 397-407

Author(s):

Lhoussain El Fadil

Keyword(s):

Number Field ◽

Irreducible Polynomial ◽

Number Fields ◽

Rational Integer ◽

Complex Root ◽

Integral Bases ◽

Pure Number

AbstractLet K = ℚ(α) be a number field generated by a complex root α of a monic irreducible polynomial f(x) = x24 – m, with m ≠ 1 is a square free rational integer. In this paper, we prove that if m ≡ 2 or 3 (mod 4) and m ≢∓1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 4) or m ≡ 1 (mod 9), then the number field K is not monogenic.

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On power integral bases for certain pure number fields defined by x2r.5s−m

Communications in Algebra ◽

10.1080/00927872.2021.1883642 ◽

2021 ◽

pp. 1-11

Author(s):

Hamid Ben Yakkou ◽

Abdelhakim Chillali ◽

Lhoussain El Fadil

Keyword(s):

Number Fields ◽

Integral Bases ◽

Pure Number

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On power integral bases of certain pure number fields defined by $$x^{3^r} - m$$

São Paulo Journal of Mathematical Sciences ◽

10.1007/s40863-021-00251-2 ◽

2021 ◽

Author(s):

Hamid Ben Yakkou ◽

Omar Kchit

Keyword(s):

Number Fields ◽

Integral Bases ◽

Pure Number

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Power Integral Bases in Composits of Number Fields

Canadian Mathematical Bulletin ◽

10.4153/cmb-1998-025-3 ◽

1998 ◽

Vol 41 (2) ◽

pp. 158-165 ◽

Cited By ~ 9

Author(s):

István Gaál

Keyword(s):

Number Fields ◽

Parametric Family ◽

Prime Degree ◽

Index Form ◽

Form Equation ◽

Integral Bases ◽

Quadratic Extensions ◽

Totally Real

AbstractIn the present paper we consider the problem of finding power integral bases in number fields which are composits of two subfields with coprime discriminants. Especially, we consider imaginary quadratic extensions of totally real cyclic number fields of prime degree. As an example we solve the index form equation completely in a two parametric family of fields of degree 10 of this type.

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