Integral Bases and Monogenity of Pure Number Fields with Non-Square Free Parameters up to Degree 9

Abstract

AbstractLetKbe a pure number field generated by a rootαof a monic irreducible polynomialf(x)=xn−mwithma rational integer and 3≤n≤ 9 an integer. In this paper, we calculate an integral basis of ℤK, and we study the monogenity ofK, extending former results to the case whenmis not necessarily square-free. Collecting and completing the corresponding results in this more general case, our purpose is to provide a parallel to [Gaál, I.—Remete, L.:Power integral bases and monogenity of pure fields,J.Number Theory,173(2017), 129–146], where only square-free values ofmwere considered.