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On Index and Monogenity of Certain Number Fields Defined by Trinomials

  • Lhoussain El Fadil
Veröffentlicht/Copyright: 4. August 2023
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ABSTRACT

Let K be a number field generated by a root θ of a monic irreducible trinomial F(x)=xn+axm+b[x] . In this paper, we study the problem of monogenity of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic. As applications, we show that there are infinite families of non-monogenic number fields defined by trinomials of degree n = 2 r · 3 k with r and k two positive integers. We also give infinite families of non-monogenic sextic number fields defined by trinomials. Some illustrating examples are giving at the end of this paper.

2020 Mathematics Subject Classification: Primary 11R04; Secondary 11R21; 11Y40

(Communicated by István Gaál)


Acknowledgement

The author is deeply grateful to the anonymous referees whose valuable comments and suggestions have tremendously improved the quality of this paper. As well as for Professor István Gaál for his encouragement and advice and for Enric Nart who introduced him to Newton polygon techniques.

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Received: 2022-05-31
Accepted: 2022-09-23
Published Online: 2023-08-04

© 2023 Mathematical Institute Slovak Academy of Sciences

Heruntergeladen am 16.12.2025 von https://www.degruyterbrill.com/document/doi/10.1515/ms-2023-0063/pdf
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