On the category of modules of Gorenstein dimension zero II
On the category of modules of Gorenstein dimension zero II
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DOI：
10.1016/j.jalgebra.2003.11.011
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发表时间：
2004-08
影响因子：
0.9
通讯作者：
Ryo Takahashi
中科院分区：
文献类型：
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作者：
Ryo Takahashi
令 R 为交换诺特亨塞尔非戈伦斯坦局部环。作者在[R. Takahashi，《关于 Gorenstein 零维模的范畴》，预印本，2003]如果存在 Gorenstein 零维非自由模，则存在无穷多个 Gorenstein 零维不可分解 R 模的同构类，并证明了当 R 深度为零时该猜想成立。在本文中，我们证明当 R 的深度为 1 时，该猜想也成立。
Let R be a commutative noetherian henselian non-Gorenstein local ring. The author has conjectured in [R. Takahashi, On the category of modules of Gorenstein dimension zero, preprint, 2003] that there exist infinitely many isomorphism classes of indecomposable R-modules of Gorenstein dimension zero if there exists a non-free module of Gorenstein dimension zero, and has proved that the conjecture holds when R has depth zero. In this paper, we prove that the conjecture also holds when R has depth one.