Monogenity and Power Integral Bases: Recent Developments

TL;DR

This paper reviews recent advances in algebraic number theory focusing on monogenity and power integral bases, summarizing new results, methods, and open problems from recent research and conferences.

Contribution

It compiles recent results, methods, and open problems in the study of monogenity and power integral bases, highlighting ongoing research developments.

Findings

Compilation of recent research results

Overview of methods used in the field

Identification of open problems for future work

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.