On power integral bases for certain pure number fields defined by x2r.5s−m

Abstract

Let K=Q(α) be a pure number field generated by a root α of a monic irreducible polynomial F(x)=x2r·5s−m, with m≠∓1 is a square free integer, r and s are two positive integers. In this article, we study the monogenity of K. We prove that if m≡1(mod 4) and m¯∉{1¯,7¯,18¯,24¯}(mod 25), then K is monogenic. We give also sufficient conditions on r, s, and m for K to be not monogenic. Some illustrating examples are given too.

Topics & Concepts