vix.ing · top · new · best · stats · spec

On Power integral bases for certain pure number fields

2020/06/19 by Fadil, L. El
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2006.11230

Abstract

Let K=ℚ(α) be a number field generated by a complex root α of a monic irreducible polynomial f(x)=x¹²-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\not≡ ∓ 1 (mod 9), then the number field K is monogenic. If m ≡ 1 (mod 8) or m≡ ∓ 1 (mod 9), then the number field K is not monogenic.

On power integral bases of certain pure number fields defined by X⁶⁰-m
On power integral bases of certain pure number fields defined by x^{2^u⋅3^v}-m
On monogenity of certain pure number fields defined by x^{p^r}-m
On integral bases and monogenity of pure octic number fields with non-square free parameters
On monogenity of certain pure number fields defined by x^{2^u⋅ 3^v⋅ 5^t}-m

On Power integral bases for certain pure number fields

Abstract

Related