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

Lhoussain El Fadil and István Gaál ()
Additional contact information
Lhoussain El Fadil: Faculty of Sciences Dhar El Mahraz, Sidi Mohamed ben Abdellah University, Atlas-Fes P.O. Box 1796, Morocco
István Gaál: Institute of Mathematics, University of Debrecen, H-4032 Debrecen, Hungary

Mathematics, 2025, vol. 13, issue 6, 1-19

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.

Keywords: power integral bases; theorem of Ore; prime ideal factorization; common index divisor (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/6/905/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/6/905/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:6:p:905-:d:1607961

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().