Research Article

On common index divisor and monogenity of certain number fields defined by trinomials X 6 + AX + B

Published in: Quaestiones Mathematicae
Volume 46 , issue 8 : Entrepreneurship and Africa’s Cultural Context , 2024 , pages: 1609–1627
DOI: 10.2989/16073606.2022.2110537
Author(s): Lhoussain El Fadil Sidi mohamed ben Abdellah University, Morocco,
Keywords: 11R04, 11Y40, 11R09, 11R21, Power integral bases, theorem of Ore, prime ideal factorization, common index divisor,
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Abstract

For a number field K defined by a trinomial F (x) = x 6 + ax + b ∈ ℤ[x], Jakhar and Kumar gave some necessary conditions on a and b, which guarantee the non-monogenity of K [25]. In this paper, for every prime integer p, we characterize when p is a common index divisor of K. In particular, if any one of these conditions holds, then K is not monogenic. In such a way our proposed results extend those of Jakhar and Kumar.
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