论文标题
由X^6+ax+b定义的六字段的判别和积分基础
Discriminant and Integral basis of sextic fields defined by x^6+ax+b
论文作者
论文摘要
令$ k = \ mathbb q（θ）$是一个代数数字字段，$θ$带有不可减至的trinomial $ f（x）= x^6+ax+b $属于$ \ mathbb {z z} [x] $。在本文中，对于每个质数$ p $，我们计算了$ p $的最高功率，在$ k $的判别中，划分为$ a，〜b $ a，〜b $和$ f（x）$的判别。还为每个Prime $ P $提供了$ K $的明确$ p $ - 构成基础，并描述了一种方法是从这些$ p $ integral bases获得$ k $的积分基础，并用示例说明。
Let $K=\mathbb Q(θ)$ be an algebraic number field with $θ$ a root of an irreducible trinomial $f(x)=x^6+ax+b$ belonging to $\mathbb{Z}[x]$. In this paper, for each prime number $p$ we compute the highest power of $p$ dividing the discriminant of $K$ in terms of the prime powers dividing $a,~b$ and discriminant of $f(x)$. An explicit $p$-integral basis of $K$ is also given for each prime $p$ and a method is described to obtain an integral basis of $K$ from these $p$-integral bases which is illustrated with examples.
