局部二次变换的无穷有向并的渐近性质
Asymptotic properties of infinite directed unions of local quadratic transforms
摘要：
考虑正则局部环的连续局部二次变换的无穷序列{R_n}。设S表示正则局部环序列R_n的有向并.我们以前证明了序列的阶赋值环族的唯一极限点V的存在性。在本文中，我们研究了这个家庭的顺序估值的渐近性质。我们联系这一渐近行为的环理论性质的S，即是否S是阿基米德和S是否是完全整闭。我们构造这样的S的例子，是阿基米德和完全整闭，但不是赋值域。我们给出了一个明确的描述V，其中的描述取决于S是否是阿基米德或非阿基米德。
英文摘要：
We consider infinite sequences {R_n} of successive local quadratic transforms of a regular local ring. Let S denote the directed union of the sequence of regular local rings R_n. We previously showed the existence of a unique limit point V of the family of order valuation rings of the sequence. In this paper, we examine asymptotic properties of this family of order valuations. We link this asymptotic behavior to ring-theoretic properties of S, namely whether S is archimedean and whether S is completely integrally closed. We construct examples of such S that are archimedean and completely integrally closed but not valuation domains. We give an explicit description of V, where the description depends on whether S is archimedean or non-archimedean.
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