June 2023 ON NONMONOGENIC NUMBER FIELDS DEFINED BY TRINOMIALS OF TYPE xn+axm+b
Hamid Ben Yakkou
Rocky Mountain J. Math. 53(3): 685-699 (June 2023). DOI: 10.1216/rmj.2023.53.685

Abstract

Let K=(𝜃) be a number field generated by a complex root 𝜃 of a monic irreducible trinomial F(x)=xn+axm+b[x]. In this paper, we deal with the problem of the nonmonogenity of K. More precisely, we provide some explicit conditions on a, b, n, and m for which K is not monogenic. As an application, we show that there are infinite families of nonmonogenic number fields defined by trinomials of degrees n=s2r3k, where s, r, and k are positive integers. Finally, we illustrate our results by giving some examples.

Citation

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Hamid Ben Yakkou. "ON NONMONOGENIC NUMBER FIELDS DEFINED BY TRINOMIALS OF TYPE xn+axm+b." Rocky Mountain J. Math. 53 (3) 685 - 699, June 2023. https://doi.org/10.1216/rmj.2023.53.685

Information

Received: 25 April 2022; Revised: 11 July 2022; Accepted: 9 August 2022; Published: June 2023
First available in Project Euclid: 21 July 2023

MathSciNet: MR4617905
zbMATH: 07731139
Digital Object Identifier: 10.1216/rmj.2023.53.685

Subjects:
Primary: 11R04 , 11R16 , 11R21

Keywords: common index divisor , monogenity , power integral basis , prime ideal factorization , theorem of Ore , trinomials

Rights: Copyright © 2023 Rocky Mountain Mathematics Consortium

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Vol.53 • No. 3 • June 2023
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