On canonical number systems and monogenity of pure number fields

Let m be a rational integer (m ≠ 0, ± 1) and consider a pure number field K = Q (√[n]m) with n ≥ 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 {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 {BFC, BF, HNHCNS}.