On canonical number systems and monogenity of pure number fields (2407.00819v1)

Abstract: Let $m$ be a rational integer $(m \neq 0, \pm 1)$ and consider a pure number field $K = \mathbb{Q} (\sqrt[n]{m}) $ with $n \ge 3$. Most papers discussing the monogenity of pure number fields focus only on the case where $m$ is square-free. In this paper, based on a classical theorem of Ore on the prime ideal decomposition \cite{MN92, O}, we study the monogenity of $K$ with $m$ is not necessarily square-free. As an application, several examples of the application of monogenic fields to CNS (Canonical Number System) are shown. In this way, our results extend some parts of previously established results \cite{BFC, BF, HNHCNS}.