论文标题
关于三项元素定义的某些数字字段的索引分隔符和单基因$ x^7+ax+b $
On index divisors and monogenity of certain number fields defined by trinomials $x^7+ax+b$
论文作者
论文摘要
对于由TrinoMail $ f（x）= x^7+ax+b \ in \ mathbb {z} [x] $，$ f（x）$ f（x）$ f（x）$ f（x] $，$ khar和kumar在$ a $ a和$ b $上提供了一些必要的条件，这保证$ k $ \ cite {a6}的非单调性。在本文中，对于每个Prime Integer $ P $，我们都表征$ p $是$ k $的常见指数除数。特别是，如果这些条件中的任何一种，则$ k $不是单基因。通过这种方式，我们提出的结果扩大了雅加尔和库马尔的结果。
For a number field $K$ defined by a trinomail $F(x) = x^7+ax+b \in \mathbb{Z}[x]$, Jakhar and Kumar gave some necessary conditions on $a$ and $b$, which guarantee the non-monogenity of $K$ \cite{A6}. In this paper, for every prime integer $p$, we characterize when $p$ is a common index divisor of $K$. In particular, if any one of these conditions holds, then $K$ is not monogenic. In such a way our proposed results extend those of Jakhar and Kumar.
