论文标题
在索引划分和由$ x^{12}+ax^m+b $定义的某些数字字段的单基因上
On index divisors and monogenity of certain number fields defined by $x^{12}+ax^m+b$
论文作者
论文摘要
在本文中，我们处理由monic不可约三项元素定义的数字字段的问题，$ f（x）= x^{12}+ax^m+b \ in \ mathbb {z} [x] $，$ 1 \ leq m \ leq m \ leq11 $。我们在$ a $，$ b $和$ m $的情况下提供足够的条件，以使数字字段$ k $不是单一的。特别是，对于$ m = 1 $，对于每个有理prime $ p $，我们都会表征$ p $划分$ k $的索引，我们为这些数字字段的narkiewicz \ cite {nar}提供部分答案。我们的结果通过计算示例来说明。
In this paper, we deal with the problem of monogenity of number fields defined by monic irreducible trinomials $F(x)=x^{12}+ax^m+b\in \mathbb{Z}[x]$ with $1\leq m\leq11$. We give sufficient conditions on $a$, $b$, and $m$ so that the number field $K$ is not monogenic. In particular, for $m=1$ and for every rational prime $p$, we characterize when $p$ divides the index of $K$ and we provide a partial answer to the Problem $22$ of Narkiewicz \cite{Nar} for these number fields. Our results are illustrated by computational examples.
