论文标题
一些质量学位的分裂符号代数
Some split symbol algebras of prime degree
论文作者
论文摘要
令$ p $为奇数，让$ k = \ mathbb {q}（ε）$，其中$ε$是统一的原始立方根，而让$ l $为kummer field $ \ mathbb {q} \ left（ε，\ sqrt [3]αα\ right）$。在本文中，我们获得了符号代数$ \ left（\ frac {α，p} {k，ε} \ right）$和$ \ left（\ frac {α，p^{ $ cl \ left（l \ right）$的$ \ mathcal {o} _l $的Prime Ideal，该$ p \ Mathcal {o} _l。
Let $p$ be an odd prime, let $K=\mathbb{Q}(ε)$ where $ε$ is a primitive cubic root of unity, and let $L$ be the Kummer field $\mathbb{Q}\left(ε, \sqrt[3]α\right)$. In this paper we obtain a characterization of the splitting behavior of the symbol algebras $\left( \frac{α,p}{K,ε}\right)$ and $\left( \frac{α,p^{h_{p}}}{K,ε}\right)$, where $h_{p}$ is the order in the class group $Cl\left(L\right)$ of a prime ideal of $\mathcal{O}_L$ which divides $p\mathcal{O}_L.$
