On the Monogenity of Quartic Number Fields Defined by x4 + ax2 + b
Year: 2025
Type: article
Abstract: For any quartic number field K generated by a root α of an irreducible trinomial of type x4+ax2+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.
Source: Mathematics
DOI: 10.3390/math13060905
Authors: Lhoussain El Fadil, István Gaál
Institutions: Sidi Mohamed Ben Abdellah University, University of Debrecen
Language: English
Subfield: Geometry and Topology
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W4408167684