In all available papers, on power integral bases of any pure sextic number fields K generated by α a complex root of a monic irreducible polynomial $f(x)=x^6-m\in \mathbb{Z}[x]$, it was assumed that the rational integer $m\ne \mp 1$ is square free. In this paper, we investigate the monogeneity of any pure sextic number field, where the condition m is a square free rational integer is omitted. We start by calculating an integral basis of ${\mathbb{Z}}_K$; the ring of integers of K. In particular, we characterize when ${\mathbb{Z}}_K=\mathbb{Z}[\alpha ]$, that is when ${\mathbb{Z}}_K$ is monogenic and generated by α. We give sufficient conditions on m, which warranty that K is not monogenic. We finish the paper by investigating the case, where $m=e^5$ and $e\ne \mp 1$ is a square free rational integer.

在所有可用的论文中，在由α生成的任何纯正弦数场K的幂积分基础上，它是一元不可约多项式的复数根$F（X）=X^6-米\in \mathbb{ž}[X]$，假设有理整数 $米\ne \mp \mathrm{1个}$没有正方形。在本文中，我们研究了任何纯正六边形字段的均一性，其中条件m是一个正方形，但省略了有理整数。我们首先计算${\mathbb{ž}}_{ķ}$; K的整数环。特别是，我们描述了什么时候${\mathbb{ž}}_{ķ}=\mathbb{ž}[\alpha ]$，那是什么时候 ${\mathbb{ž}}_{ķ}$是单基因的，由α生成。我们对m给出足够的条件，该条件保证K不是单基因的。我们通过调查此案来完成本文，其中$米={Ë}^5$ 和 $Ë\ne \mp \mathrm{1个}$ 是一个平方自由有理整数。