Generalized tilting modules with finite injective dimension

2006/02/25 by Zhaoyong Huang, Huang, Zhaoyong · 2 citations
Mathematics · Physics and Astronomy · #16E10 #16E30 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.math/0602572

openalex publication_date 2006/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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, we describe when the subcategory \\rm Ext_Sⁿ(N, U)|N is a finitely generated right S-module\ is closed under submodules. As a consequence, we obtain a negative answer to a question posed by Auslander in 1969. Finally, some partial answers to Wakamatsu Tilting Conjecture are given.

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• Cotilting invariance of the Auslander-Reiten conjecture
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