论文标题
关于索引除数和一定数量字段的单个字段
On index divisors and monogenity of certain number fields defined by trinomials
论文作者
论文摘要
令$ k $为一个数字字段，该数字由一个mon不可减少的三项元素$ f（x）= x^n+ax^{m}+b \ in \ z [x] $生成的数字字段。在本文中，我们研究了$ k $的问题。更确切地说，我们为$ a $，$ b $，$ n $和$ m $提供一些明确的条件，$ k $不是单基因。作为应用程序，我们表明，有一个无单性数字字段的家族，由$ n = 2^r \ cdot3^k $定义，带有$ r $，$ r $和$ k $ $两个正整数。我们还提供了由三项元素定义的非发电性六号字段的无限家族。本文结尾处有一些说明的例子。
Let $K$ be a number field generated by a root $þ$ of a monic irreducible trinomial $F(x) = x^n+ax^{m}+b \in \Z[x]$. In this paper, we study the problem of $K$. More precisely, we provide some explicit conditions on $a$, $b$, $n$, and $m$ for which $K$ is not monogenic. As applications, we show that there are infinite families of non-monogenic number fields defined by trinomials of degree $n=2^r\cdot3^k$ with $r$ and $k$ two positive integers. We also give infinite families of non-monogenic sextic number fields defined by trinomials. Some illustrating examples are giving at the end of this paper.
