JP Journal of Algebra, Number Theory and Applications
Volume 24, Issue 1, Pages 105 - 114
(February 2012)
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POWER INTEGRAL BASES IN PARAMETRIC FAMILIES OF BIQUADRATIC FIELDS
István Gaál and Tímea Szabó
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Abstract: We consider two families of totally complex biquadratic fields depending on two parameters which were recently considered by Huard et al. [8]. Using our general method [4] and the integral basis described by [8], we solve the index form equations in a parametric form in these families and prove that (up to equivalence), they admit only one generator of power integral bases. Note that these are the first families of number fields with two parameters where all generators of power integral bases are determined. |
Keywords and phrases: biquadratic fields, power integral bases. |
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