Approximately Cohen-Macaulay Rings
Approximately Cohen-Macaulay Rings
复制标题
近似科恩-麦考利环
DOI：
10.1016/0021-8693(82)90248-4
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发表时间：
1982
影响因子：
0.9
通讯作者：
S. Goto
中科院分区：
文献类型：
--
作者：
S. Goto
设A是具有极大理想m且d= dim A的Noether局部环.本文的目的是研究当存在m的元素a使得A/a”，4是d-1维Cohen-Macaulay环时，对任意整数n> 0.回想一下，A是Gorenstein当（且仅当）存在m的元素a使得A/a”A是d-1维的Gorenstein环，对于每个整数n> 0（参见，例如，131）。显然，科恩-麦考利案并非如此。然而，由于这样的环可以说近似于Cohen-Macaulay，并且可能非常特殊，所以澄清给定的环A何时具有此性质似乎很有趣。
Let A be a Noetherian local ring with maximal ideal m and d= dim A. The purpose of this note is to study when there is an element a of m such that A/a”, 4 is a Cohen-Macaulay ring of dimension d-1 for every integer n> 0. Recall that A is Gorenstein if (and only if) there is an element a of m such that A/a” A is a Gorenstein ring of dimension d-1 for every integer n> 0 (cf., eg, 131). Clearly this is not true in the Cohen-Macaulay case. However, since such rings are, so to speak, approximately Cohen-Macaulay and may be pretty special, it seems interesting to clarify when a given ring A has this property.