On power integral bases for certain pure number fields defined by x24 – m
Lhoussain El Fadil
Abstract
Abstract Let K = ℚ( α ) be a number field generated by a complex root α of a monic irreducible polynomial f ( x ) = x 24 – 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.
Topics & Concepts
MathematicsMonic polynomialModInteger (computer science)Algebraic number fieldField (mathematics)Rational numberCombinatoricsSquare rootIrreducible polynomialFinite fieldSquare (algebra)Discrete mathematicsPolynomialPure mathematicsMathematical analysisMatrix polynomialGeometryProgramming languageComputer scienceAlgebraic Geometry and Number TheoryCoding theory and cryptographyAdvanced Differential Equations and Dynamical Systems