Power Integral Bases in Orders of Composite Fields

Abstract

We consider the existence of power integral bases in composites of polynomial orders of number fields. We prove that if the degree of the composite field equals the product of the degrees of its subfields and the minimal polynomials of the generating elements of the polynomial orders have a multiple linear factor in their factorization modulo q, then the composite order admits no power integral bases. As an application we provide several examples including a parametric family of "simplest sextic fields.''