scholarly journals On the Genus Fields of Pure Number Fields II

1981 ◽  
Vol 04 (1) ◽  
pp. 213-220
Author(s):  
Makoto ISHIDA
Keyword(s):  
Number Fields ◽  
Pure Number

scholarly journals ON INTEGRAL BASIS OF PURE NUMBER FIELDS

Mathematika ◽  
2020 ◽  
Vol 67 (1) ◽  
pp. 187-195
Author(s):  
Anuj Jakhar ◽  
Sudesh K. Khanduja ◽  
Neeraj Sangwan
Keyword(s):  
Number Fields ◽  
Integral Basis ◽  
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 monogenity of certain pure number fields defined by xpr − m

2021 ◽  
Author(s):  
Hamid Ben Yakkou ◽  
Lhoussain El Fadil
Keyword(s):  
Positive Integer ◽  
Number Field ◽  
Irreducible Polynomial ◽  
Number Fields ◽  
Rational Integer ◽  
Complex Root ◽  
Prime Integer ◽  
Pure Number ◽  
Polynomial Formula

Let [Formula: see text] be a pure number field generated by a complex root [Formula: see text] of a monic irreducible polynomial [Formula: see text] where [Formula: see text] is a square free rational integer, [Formula: see text] is a rational prime integer, and [Formula: see text] is a positive integer. In this paper, we study the monogenity of [Formula: see text]. We prove that if [Formula: see text], then [Formula: see text] is monogenic. But if [Formula: see text] and [Formula: see text], then [Formula: see text] is not monogenic. Some illustrating examples are given.

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