An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules
An Uncountably Infinite Number of Indecomposable Totally Reflexive Modules
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DOI：
10.1017/s0027763000025836
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发表时间：
2006-07
影响因子：
0.8
通讯作者：
Ryo Takahashi
中科院分区：
文献类型：
--
作者：
Ryo Takahashi
几年前，Huneke和Leuschke证明了一个解决Schreyer猜想的定理。它断言，一个完备的或具有不可数剩余域的可数科恩-麦考利型的优秀科恩-麦考利局部环最多有一个一维奇异轨迹。本文证明了可以去掉关于这一优良性质的假设，并在任意局部环上讨论了这一定理。本文的主要目的是证明某个素理想和某个全自反模的存在蕴含着不可分解的全自反模的同构类的不可数无穷个的存在性。
Abstract Several years ago, Huneke and Leuschke proved a theorem solving a conjecture of Schreyer. It asserts that an excellent Cohen-Macaulay local ring of countable Cohen-Macaulay type which is complete or has uncountable residue field has at most a one-dimensional singular locus. In this paper, it is verified that the assumption of the excellent property can be removed, and the theorem is considered over an arbitrary local ring. The main purpose of this paper is to prove that the existence of a certain prime ideal and a certain totally reflexive module implies the existence of an uncountably infinite number of isomorphism classes of indecomposable totally reflexive modules.