论文标题
关于由$ x^4+ax^2+b $定义的四分位数字段的单基因
On the monogenity of quartic number fields defined by $x^4+ax^2+b$
论文作者
论文摘要
对于由dyble type $ x^4+ax^2+b \ y z [x] $的root $α$生成的任何四分位数字段$ k $，当$ z [α] $完全关闭时，我们会表征。同样对于$ p = 2,3 $，我们明确地赋予了$ p $ i（k）$的最高功率，$ k $的普通指数除数。对于这种类型的一系列单基因三项元素，我们证明到等效性，$ k = q（α）$中只有一个幂积分碱基的发生器。我们用一系列示例来说明我们的陈述。
For any quartic number field $K$ generated by a root $α$ of an irreducible trinomial of type $x^4+ax^2+b\in Z[x]$, we characterize when $Z[α]$ is integrally closed. Also for $p=2,3$, we explicitly give the highest power of $p$ dividing $i(K)$, the common index divisor of $K$. For a wide class of monogenic trinomials of this type we prove that up to equivalence there is only one generator of power integral bases in $K=Q(α)$. We illustrate our statements with a series of examples.
