PDF files of articles are only available for institutions which have paid for the online version upon signing an Institutional User License.

On power integral bases for certain pure number fields defined by $x^{2\cdot 3^k}-m$

Volume 201 / 2021

Lhoussain El Fadil Acta Arithmetica 201 (2021), 269-280 MSC: Primary 11R04, 11R21; Secondary 11Y40. DOI: 10.4064/aa210402-8-5 Published online: 4 November 2021


Let $K=\mathbb Q (\alpha )$ be the number field generated by a complex root $\alpha $ of a monic irreducible polynomial $f(x)=x^{2\cdot 3^k}-m$ with {$m\neq \pm 1$} a square free rational integer and $k$ a positive integer. We prove that if $m \equiv 2 \mbox { or } 3\def\md#1{\ \mbox{(mod }{#1})}\md 4$ and {$m\not \equiv \pm 1\def\md#1{\ \mbox{(mod }{#1})}\md 9$}, then the field $K$ is monogenic, while if $m \equiv 1\def\md#1{\ \mbox{(mod }{#1})}\md 4$ or $m\equiv 1\def\md#1{\ \mbox{(mod }{#1})}\md 9$ or $k\ge 3$ and $m\equiv -1\def\md#1{\ \mbox{(mod }{#1})}\md {81}$, then $K$ is not monogenic.


  • Lhoussain El FadilDepartment of Mathematics
    Faculty of Sciences Dhar El Mahraz
    Sidi Mohammed ben Abdellah University
    Fes, Morocco

Search for IMPAN publications

Query phrase too short. Type at least 4 characters.

Rewrite code from the image

Reload image

Reload image