On index divisors and monogenity of certain number fields defined by trinomials x⁷+ax+b

2022/02/18 by Fadil, Lhoussain El
#11Y04 #D.2 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2202.09342

Abstract

For a number field K defined by a trinomail F(x) = x⁷+ax+b ∈ ℤ[x], Jakhar and Kumar gave some necessary conditions on a and b, which guarantee the non-monogenity of K \citeA6. 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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