Geodesic
On nonmonogenic number fields defined by $x^6+ax+b$
Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 788-794

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DOI

Let q be a prime number and $K = \mathbb Q(\theta )$ be an algebraic number field with $\theta $ a root of an irreducible trinomial $x^{6}+ax+b$ having integer coefficients. In this paper, we provide some explicit conditions on $a, b$ for which K is not monogenic. As an application, in a special case when $a =0$, K is not monogenic if $b\equiv 7 \mod 8$ or $b\equiv 8 \mod 9$. As an example, we also give a nonmonogenic class of number fields defined by irreducible sextic trinomials.
DOI : 10.4153/S0008439521000825
Mots-clés : Monogenity, nonmonogenity, Newton polygon, power basis 
Jakhar, Anuj; Kumar, Surender. On nonmonogenic number fields defined by $x^6+ax+b$. Canadian mathematical bulletin, Tome 65 (2022) no. 3, pp. 788-794. doi: 10.4153/S0008439521000825
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     title = {On nonmonogenic number fields defined by $x^6+ax+b$},
     journal = {Canadian mathematical bulletin},
     pages = {788--794},
     year = {2022},
     volume = {65},
     number = {3},
     doi = {10.4153/S0008439521000825},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/S0008439521000825/}
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