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MONOGENITY OF THE COMPOSITION OF POLYNOMIALS

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  08 May 2025

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Abstract

One of the important problems in algebraic number theory is to study the monogenity of number fields. Monogenic number fields arise from the roots of monogenic polynomials. In this article, we deal with the problem of monogenity of the composition of two monic polynomials having integer coefficients. We provide necessary and sufficient conditions for the composition to be monogenic together with a further sufficient condition. At the end of the paper, we construct an infinite tower of monogenic number fields.

Keywords

monogenitydiscriminantresultant

MSC classification

Primary: 11R04: Algebraic numbers; rings of algebraic integers
Secondary: 11R21: Other number fields
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , First View , pp. 1 - 9
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Australian Mathematical Publishing Association Inc.

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