Modules of G-Dimension Zero over Local Rings with the Cube of Maximal Ideal Being Zero
Modules of G-Dimension Zero over Local Rings with the Cube of Maximal Ideal Being Zero
复制标题
DOI：
10.1007/978-94-007-1092-4_16
复制
发表时间：
2003-03
期刊：
影响因子：
--
通讯作者：
Y. Yoshino
中科院分区：
文献类型：
--
作者：
Y. Yoshino
设（R，m）是交换Noether局部环，m3=（0）.给出了R存在G维为零的非自由模的一个条件。我们还将在射影空间的开子集中构造一族带参数的G维零非同构不可分解模。最后，我们将证明R上G维为零的模所构成的子范畴不一定是R-生成的R-模范畴中的逆变有限子范畴。
Let(R,m)be a commutative Noetherian local ring with m3= (0). We give a condition forRto have a non-free module of G-dimension zero. We shall also construct a family of non- isomorphic indecomposable modules of G-dimension zero with parameters in an open subset of pro- jective space. We shall finally show that the subcategory consisting of modules of G-dimension zero overRis not necessarily a contravariantly finite subcategory in the category of finitely generatedR-modules.