二维正则局部环的二次变换树
The tree of quadratic transforms of a regular local ring of dimension two
摘要：
设$D$是一个二维正则局部环，$Q(D)$表示$D$的二维正则局部覆盖环的二次树.我们探讨的拓扑结构的树$Q(D)$和家庭${\mathcal{R}}(D)$的环作为交叉点的环在$Q(D)$。若$A$是$ Q(D)$中环的有限交，则$A$是Noether的，并且$A$的结构是很好理解的.然而，${\mathcal{R}}(D)$中的其他环不需要是诺特环。本文的两个主要目标是检查拓扑性质的二次树$Q(D)$，并检查环的结构在集合${\mathcal{R}}(D)$。
英文摘要：
Let $D$ be a 2-dimensional regular local ring and let $Q(D)$ denote the quadratic tree of 2-dimensional regular local overrings of $D$. We explore the topology of the tree $Q(D)$ and the family ${\mathcal{R}}(D)$ of rings obtained as intersections of rings in $Q(D)$. If $A$ is a finite intersection of rings in $ Q(D)$, then $A$ is Noetherian and the structure of $A$ is well understood. However, other rings in ${\mathcal{R}}(D)$ need not be Noetherian. The two main goals of this paper are to examine topological properties of the quadratic tree $Q(D)$, and to examine the structure of rings in the set ${\mathcal{R}}(D)$.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
