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

2021 ◽  
Author(s):  
Lhoussain El Fadil
2021 ◽  
Vol 58 (3) ◽  
pp. 371-380
Author(s):  
Lhoussain El Fadil

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.


2020 ◽  
Vol 57 (3) ◽  
pp. 397-407
Author(s):  
Lhoussain El Fadil

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.


2021 ◽  
pp. 1-11
Author(s):  
Hamid Ben Yakkou ◽  
Abdelhakim Chillali ◽  
Lhoussain El Fadil

1998 ◽  
Vol 41 (2) ◽  
pp. 158-165 ◽  
Author(s):  
István Gaál

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.


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

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