Generalized tilting modules with finite injective dimension

Details Generalized tilting modules with finite injective dimension Generalized tilting modules with finite injective dimension

2006-02-25

arxiv.org/abs/math/0602572v3

Mathematics

Rings and Algebras

18 pages. This is the final version. To appear in Journal of Algebra

Scientific paper

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 $\{{\rm Ext}_S^n(N, U)|N$ 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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