First-degree prime ideals of composite extensions
First-degree prime ideals of composite extensions
Let $\mathbb{Q}(\alpha)$ and $\mathbb{Q}(\beta)$ be linearly disjoint number fields and let $\mathbb{Q}(\theta)$ be their compositum. We prove that the first-degree prime ideals of $\mathbb{Z}[\theta]$ may almost always be constructed in terms of the first-degree prime ideals of $\mathbb{Z}[\alpha]$ and $\mathbb{Z}[\beta]$, and vice-versa. We also classify the cases in which this …