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Power Integral Bases in Orders of Composite Fields

2002; Taylor & Francis; Volume: 11; Issue: 1 Linguagem: Inglês

10.1080/10586458.2002.10504471

ISSN

1944-950X

Autores

István Gaál, Páter Olajos, Michael Pohst,

Tópico(s)

Advanced Differential Equations and Dynamical Systems

Resumo

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." Keywords: Composite fieldspower integral bases

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