JP Journal of Algebra, Number Theory and Applications
Volume 39, Issue 3, Pages 307 - 326
(June 2017) http://dx.doi.org/10.17654/NT039030307 |
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DETERMINING ELEMENTS OF MINIMAL INDEX IN AN INFINITE FAMILY OF TOTALLY REAL BICYCLIC BIQUADRATIC NUMBER FIELDS
István Gaál and Borka Jadrijević
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Abstract: Let be a positive integer such that c and are square-free. We consider the infinite parametric family of bicyclic biquadratic fields We determine the integral basis of the field. We show that K admits no power integral basis, determine the minimal index and all elements of minimal index. We use the solutions of a parametric family of quartic Thue equations and extensive numerical calculations by Maple and Magma. |
Keywords and phrases: bicyclic biquadratic fields, power integral basis, minimal index. |
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