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Selforthogonal Modules with Finite Injective Dimension III

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Abstract

Let R be a left Noetherian ring, S a right Noetherian ring and R U a generalized tilting module with S = End( R U). We give some equivalent conditions that the injective dimension of U S is finite implies that of R U is also finite. As an application, under the assumption that the injective dimensions of R U and U S are finite, we construct a hereditary and complete cotorsion theory by some subcategories associated with R U.

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Authors and Affiliations

  1. Department of Mathematics, Nanjing University, Nanjing, 210093, P. R. China

    Zhaoyong Huang

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  1. Zhaoyong Huang
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Correspondence to Zhaoyong Huang.

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Dedicated to Professor Fred Van Oystaeyen on the occasion of his sixtieth birthday.

This research was partially supported by the Specialized Research Fund for the Doctoral Program of Higher Education (Grant No. 20060284002), NSFC (Grant No. 10771095) and NSF of Jiangsu Province of China (Grant No. BK2007517).

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Huang, Z. Selforthogonal Modules with Finite Injective Dimension III. Algebr Represent Theor 12, 371–384 (2009). https://doi.org/10.1007/s10468-009-9157-2

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  • DOI: https://doi.org/10.1007/s10468-009-9157-2

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