On power integral bases for certain pure number fields defined by $x^{2\cdot 3^k}-m$

2021 ◽  
Author(s):  
Lhoussain El Fadil
Keyword(s):  
Number Fields ◽  
Integral Bases ◽  
Pure Number

On Power Integral Bases for Certain Pure Number Fields Defined by x 36 − m

2021 ◽  
Vol 58 (3) ◽  
pp. 371-380
Author(s):  
Lhoussain El Fadil
Keyword(s):  
Number Field ◽  
Irreducible Polynomial ◽  
Number Fields ◽  
Rational Integer ◽  
Complex Root ◽  
Integral Bases ◽  
Pure Number

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.

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

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.

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

2021 ◽  
pp. 1-11
Author(s):  
Hamid Ben Yakkou ◽  
Abdelhakim Chillali ◽  
Lhoussain El Fadil
Keyword(s):  
Number Fields ◽  
Integral Bases ◽  
Pure Number

Power Integral Bases in Composits of Number Fields

1998 ◽  
Vol 41 (2) ◽  
pp. 158-165 ◽  
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.

scholarly journals Existence of Integral Bases for Relative Extensions ofn-Cyclic Number Fields

1996 ◽  
Vol 60 (2) ◽  
pp. 409-416 ◽  
Author(s):  
XianKe Zhang ◽  
FuHua Xu
Keyword(s):  
Number Fields ◽  
Integral Bases
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