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On the Monogenity of Quartic Number Fields Defined by x 4 + ax 2 + b

Author

Listed:
  • Lhoussain El Fadil

    (Faculty of Sciences Dhar El Mahraz, Sidi Mohamed ben Abdellah University, Atlas-Fes P.O. Box 1796, Morocco
    These authors contributed equally to this work.)

  • István Gaál

    (Institute of Mathematics, University of Debrecen, H-4032 Debrecen, Hungary
    These authors contributed equally to this work.)

Abstract

For any quartic number field K generated by a root α of an irreducible trinomial of type x 4 + a x 2 + b ∈ Z [ x ] , we characterize when Z [ α ] is integrally closed. Also for p = 2 , 3 , we explicitly give the highest power of p dividing i ( K ) , the common index divisor of K . For a wide class of monogenic trinomials of this type, we prove that up to equivalence, there is only one generator of power integral bases in K = Q ( α ) . We illustrate our statements with a series of examples.

Suggested Citation

  • Lhoussain El Fadil & István Gaál, 2025. "On the Monogenity of Quartic Number Fields Defined by x 4 + ax 2 + b," Mathematics, MDPI, vol. 13(6), pages 1-19, March.
    • Handle: RePEc:gam:jmathe:v:13:y:2025:i:6:p:905-:d:1607961
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