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New York Journal of Mathematics
Volume 31 (2025), 619-632

  

Istvan Gaal

Power integral bases in a family of octic fields

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Published: March 31, 2025.
Keywords: monogenity; power integral basis; octic fields; relative quartic fields; relative Thue equations.
Subject [2010]: 11Y50, 11R04, 11D25.

Abstract
Several recent results prove the monogenity of some polynomials. In these cases the root of the polynomial generates a power integral basis in the number field generated by the root. A straightforward question is whether such a number field admits other generators of power integral bases? We have investigated this problem in some previous papers and here we extend this research to a family of octic polynomials, following a recent result of L. Jones [11].

Acknowledgements

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Author information

Istvan Gaal
University of Debrecen
Mathematical Institute
H-4002 Debrecen Pf.400., Hungary

gaal.istvan@unideb.hu