Gorenstein Cotilting and Tilting Modules |
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| Authors: | Liang Yan Weiqing Li |
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| Institution: | Key Laboratory of High Performance Computing and Stochastic, Information Processing (Ministry of Education of China), College of Mathematics and Computer Science, Hunan Normal University, Changsha, Hunan, China |
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| Abstract: | Auslander and Solberg introduced the concepts of finitely generated cotilting and tilting modules in relative homological algebra considering subfunctors of the Ext-functor. In this article we generalize Auslander–Solberg relative notions by giving the definitions of infinitely generated Gorenstein cotilting and tilting modules by means of Gorenstein exact sequences. Using the theory developed by Enochs on the existence of Gorenstein preenvelopes and precovers, we prove a characterization of relative Gorenstein cotilting and tilting modules, which is a generalization of the beautiful characterization of relative cotilting and tilting modules given by Bazzoni. |
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| Keywords: | m-Gorenstein cotilting modules |
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