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Generalized Tilting Modules With Finite Injective Dimension
Huang Zhaoyong * #
Nanjing University
*Correspondence author
#Submitted by
Subject: Ring Theory
Funding: 教育部博士点基金(No.20030284033)
Opened online:28 February 2006
Accepted by: none
Citation: Huang Zhaoyong.Generalized Tilting Modules With Finite Injective Dimension[OL]. [28 February 2006] http://www.paper.edu.cn/lwzx/en_releasepaper/content/5432
Let $R$ be a left noetherian ring, $S$ a right noetherian ring and $_RU$ a generalized tilting module with $S={\rm End}(_RU)$. The injective dimensions of $_RU$ and $U_S$ are identical provided both of them are finite. Under the assumption that the injective dimensions of $_RU$ and $U_S$ are finite, that the subcategory $\{ {\rm Ext}_S^n(N, U)|N$ is a finitely generated right $S$-module$\}$ is submodule closed is characterized equivalently. From which, a negative answer to a question posed by Auslander in 1969 is given. Finally, some partial answers to Wakamatsu Tilting Conjecture are given.
Keywords:generalized tilting modules, injective dimension, $U$-limit dimension, submodule closed, Wakamatsu Tilting Conjecture

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