On Biquadratic fields that admit unit power integral basis
Acta Mathematica Hungarica
We consider biquadratic number fields whose maximal orders have power integral bases consisting of units. We prove an effective and efficient criteria to decide whether the maximal order of a biquadratic field has a unit power integral basis or not. In particular we can determine all trivial biquadratic fields whose maximal orders have a unit power integral basis.
In general it is a hard problem to decide which number fields K admit power integral bases, PIB for short. In general to decide whether a number field K admits a PIB or not leads to so called index form equations.
unit sum number, additive unit structure
A. Petho, V. Ziegler (2011). On Biquadratic fields that admit unit power integral basis. Acta Math. Hungar., Pg 221–241 DOI: 10.1007/s10474-011-0103-5