Abstract: Let and According to the results of El Fadil [3], α generates a power integral basis in if and only if m is square-free, and
In this note, we consider the case m < 0 and present an efficient method to calculate generators of power integral bases in totally complex pure sextic fields. Using this method, we performed an extensive calculation for this type of fields for In these 1521 fields, we did not find any other (non-equivalent) generators of power integral bases with coefficients in absolute values in the basis
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Keywords and phrases: pure sextic fields, monogenity, power integral basis, Thue equations, calculating the solutions.
Received: February 5, 2023; Accepted: February 15, 2023; Published: February 21, 2023
How to cite this article: István Gaál, On the monogenity of totally complex pure sextic fields, JP Journal of Algebra, Number Theory and Applications 60(2) (2023), 85-96. http://dx.doi.org/10.17654/0972555523006
This Open Access Article is Licensed under Creative Commons Attribution 4.0 International License
References:
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