JP Journal of Algebra, Number Theory and Applications
Volume 47, Issue 1, Pages 87 - 98
(July 2020) http://dx.doi.org/10.17654/NT047010087 |
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MONOGENITY IN TOTALLY COMPLEX SEXTIC FIELDS, REVISITED
István Gaál
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Abstract: In addition to rather complicated general methods it is interesting and valuable to develop fast efficient methods for calculating generators of power integral bases in special types of number fields. We consider sextic fields containing real cubic and complex quadratic fields. We develop a very simple and very efficient method to calculate generators of power integral bases in this type of fields. Our method can be applied to infinite families of number fields, as well. We substantially improve the former methods. Our algorithm is illustrated with detailed examples, involving infinite parametric families. |
Keywords and phrases: monogenity, power integral basis, Thue equations, sextic fields, calculating the solutions.
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