On common index divisors and monogenity of certain number fields defined by <i>x</i><sup>5</sup> + <i>ax</i><sup>2</sup> + <i>b</i>
Lhoussain El Fadil
Abstract
Let K=Q(α) be a number field generated by a complex root α of a monic irreducible trinomial F(x)=x5+ax2+b∈Z[x]. In this paper, for every prime integer p, we give necessary and sufficient conditions on a and b so that p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic.
Topics & Concepts
MathematicsTrinomialDivisor (algebraic geometry)Integer (computer science)Monic polynomialPrime (order theory)Field (mathematics)CombinatoricsLeast common multipleMersenne primeAlgebraic number fieldGreatest common divisorFinite fieldDiscrete mathematicsRoot (linguistics)Pure mathematicsPolynomialMathematical analysisComputer scienceLinguisticsProgramming languagePhilosophyAlgebraic Geometry and Number TheoryMeromorphic and Entire FunctionsAdvanced Differential Equations and Dynamical Systems