Minimal injective resolutions of Cohen-Macaulay isolated singularities
Minimal injective resolutions of Cohen-Macaulay isolated singularities
复制标题
Cohen-Macaulay 孤立奇点的最小单射分辨率
DOI：
10.1007/s000130050394
复制
发表时间：
1999
影响因子：
0.6
通讯作者：
K. Nishida
中科院分区：
文献类型：
--
作者：
S. Goto;K. Nishida
抽象的。让
$（R，\frak {m}）$是交换Gorenstein完全局部环，其中dim R = d，设
$\Lambda $是一个R-代数，它不一定是交换的，但它是作为R-模生成的。本文给出了极小内射归结的结构
$E^\bullet _\Lambda（M）$用于
利用Cousin复形研究了$\Lambda $-格M
$C^{\bullet }_R（M）$对于M和极小的投影分解
$\Lambda ^{op}$-模块
$M^* = \hbox {Hom}_R（M，R）$，假设
$\Lambda $是一个Cohen-Macaulay孤立奇点。因此，我们得到以下结果。设R是正则局部环，令
$k \in \Bbb Z$.则环
$\Lambda $是k-Gorenstein当且仅当环
$\Delta =（R/\frak {m}）\otimes _R \Lambda $是（k - d）-Gorenstein。
Abstract. Let
$(R, \frak {m})$ be a commutative Gorenstein complete local ring with dim R = d and let
$\Lambda $ be an R-algebra which is not necessarily commutative but finitely generated as an R-module. In this paper the structure of minimal injective resolutions
$E^\bullet _\Lambda (M)$ for the
$\Lambda $-lattices M is explored, in terms of the Cousin complexes
$C^{\bullet }_R(M)$ for M and the minimal projective resolutions of the
$\Lambda ^{op}$-modules
$M^* = \hbox {Hom}_R(M,R)$ as well, under the assumption that
$\Lambda $ is a Cohen-Macaulay isolated singularity. As a consequence we get the following. Assume that R is a regular local ring and let
$k \in \Bbb Z$. Then the ring
$\Lambda $ is k-Gorenstein if and only if the ring
$\Delta = (R/\frak {m})\otimes _R \Lambda $ is (k - d)-Gorenstein.