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Volume 13
Issue 7
10.3390/axioms13070429
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Review

Monogenity and Power Integral Bases: Recent Developments

by
István Gaál
Mathematical Institute, University of Debrecen, Pf.400., H-4002 Debrecen, Hungary
Axioms 2024, 13(7), 429; https://doi.org/10.3390/axioms13070429
Submission received: 24 May 2024 / Revised: 16 June 2024 / Accepted: 24 June 2024 / Published: 26 June 2024
(This article belongs to the Special Issue Advances in Generalized Hypergeometric Functions, Integral Transforms and Number Theory)
Versions Notes

Abstract

Monogenity is a classical area of algebraic number theory that continues to be actively researched. This paper collects the results obtained over the past few years in this area. Several of the listed results were presented at a series of online conferences titled “Monogenity and Power Integral Bases”. We also give a collection of the most important methods used in several of these papers. A list of open problems for further research is also given.
Keywords: algebraic number fields; index of an element; generators of power integral bases; monogenic number fields; monogenic polynomials; pure fields; trinomials; relative extensions; algorithms algebraic number fields; index of an element; generators of power integral bases; monogenic number fields; monogenic polynomials; pure fields; trinomials; relative extensions; algorithms

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MDPI and ACS Style

Gaál, I. Monogenity and Power Integral Bases: Recent Developments. Axioms 2024, 13, 429. https://doi.org/10.3390/axioms13070429

AMA Style

Gaál I. Monogenity and Power Integral Bases: Recent Developments. Axioms. 2024; 13(7):429. https://doi.org/10.3390/axioms13070429

Chicago/Turabian Style

Gaál, István. 2024. "Monogenity and Power Integral Bases: Recent Developments" Axioms 13, no. 7: 429. https://doi.org/10.3390/axioms13070429

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