Complete Ideals in Two-Dimensional Regular Local Rings
Complete Ideals in Two-Dimensional Regular Local Rings
复制标题
二维正则局部环的完全理想
DOI：
10.1007/978-1-4612-3660-3_16
复制
发表时间：
1989
期刊：
影响因子：
--
通讯作者：
C. Huneke
中科院分区：
文献类型：
--
作者：
C. Huneke
这些笔记给出了关于二维正则局部环完全理想理论的主要事实。本文中几乎所有的定理都可以在Zariski和Samuel的交换代数卷II的附录5中找到，在Lipman的I.H.E.S.关于有理奇点的笔记中找到，或者在某些情况下在论文[G]， [R]和[H-S]中找到。大多数定理都是由Zariski和Lipman提出的。这些注释的主要目的是使这些美丽的材料更容易被不希望投入大量时间的读者理解。我们的处理与上面的处理的主要区别在于系统地使用希尔伯特-伯奇定理，并对所考虑的理想的多重性进行归纳。
These notes present the main facts concerning the theory of complete ideals in a 2-dimensional regular local ring. Almost all of the theorems in this paper can be found in Appendix 5 of Zariski and Samuel’s Commutative Algebra volume II, in Lipman’s I.H.E.S. notes on rational singularities, or in some cases the papers [G], [R], and [H-S]. Most of the theorems are due to Zariski or to Lipman. The main point of these notes is to make this beautiful material more easily accessible to a reader who does not wish to invest a large amount of time. The main difference in our treatment from the ones above is using the Hilbert-Burch theorem systematically and inducting upon the multiplicity of the ideal considered.