Calculating power integral bases by using relative power integral bases

Abstract

Let $M\subset K$ be number fields. We consider the relation of relative power integral bases of $K$ over $M$ with absolute power integral bases of $K$ over $Q$. We show how generators of absolute power integral bases can be calculated from generators of relative ones. We apply our ideas in infinite families of octic fields with quadratic subfields.

References in corpus (2)

• Calculating "small" solutions of relative Thue equations
• Calculating power integral bases by solving relative Thue equations

Cited by in corpus (1)

• Power integral bases in cubic and quartic extensions of real quadratic fields