超正规性--Krull域的推广
Perinormality -- a generalization of Krull domains
摘要：
引入一类新的整环--次正规域，它严格介于Krull域和弱正规域之间.我们建立类的基本性质，并在普遍悬链线域的情况下，我们给出了等价的perinormality的特征。（稍后，我们会指出一些只在非诺特语境中出现的微妙之处。）我们还简要地介绍和探讨了相关的概念，全球perinormality，包括与除子类群的关系。在整个过程中，我们从代数、几何和数论中提供了启发性的例子。
英文摘要：
We introduce a new class of integral domains, the perinormal domains, which fall strictly between Krull domains and weakly normal domains. We establish basic properties of the class, and in the case of universally catenary domains we give equivalent characterizations of perinormality. (Later on, we point out some subtleties that occur only in the non-Noetherian context.) We also introduce and explore briefly the related concept of global perinormality, including a relationship with divisor class groups. Throughout, we provide illuminating examples from algebra, geometry, and number theory.
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