区间环
Interval Rings
AI总结：
研究区间环，通过选取赋值环交集构造，其为二维正则局部环整闭上环，有良好性质，是二维正则局部环整闭上环分类的重要一步。
AI中文摘要：
区间环包含一类一维整闭局部整环，它们是二维正则局部环的上环。我们通过仔细选取赋值环的交集来构造它们，并证明它们具有各种良好性质。我们对这些环感兴趣是因为它们是对二维正则局部环的所有整闭上环进行分类的重要基石。
英文摘要：
Interval rings comprise a class of one-dimensional integrally closed local integral domains which are overrings of a two-dimensional regular local ring. We construct them by intersecting carefully chosen valuation rings and prove that they have various nice properties. Our interest in these rings is that they represent a major stepping stone toward classifying all integrally closed overrings of a two-dimensional regular local ring.
