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Infinitely Generated Gorenstein Tilting Modules

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Abstract

The theory of finitely generated relative (co)tilting modules has been established in the 1980s by Auslander and Solberg, and infinitely generated relative tilting modules have recently been studied by many authors in the context of Gorenstein homological algebra. In this work, we build on the theory of infinitely generated Gorenstein tilting modules by developing “Gorenstein tilting approximations” and employing these approximations to study Gorenstein tilting classes and their associated relative cotorsion pairs. As applications of our results, we discuss the problem of existence of complements to partial Gorenstein tilting modules as well as some connections between Gorenstein tilting modules and finitistic dimension conjectures.

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Acknowledgements

We thank the anonymous referee for careful reading the manuscript and helpful comments.

Part of this work was done during the first-named author’s visit to the Department of Algebra at Charles University (MFF UK) in 2018. He wishes to express his gratitude to MFF UK, especially Jan Trlifaj, for the hospitality, and University of Tehran for the financial support of the visit. The research of Siamak Yassemi is supported by Iran National Science Foundation (INSF), Project No. 95831492.

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  1. School of Mathematics, Statistics and Computer Science, University of Tehran, Tehran, Iran

    Pooyan Moradifar & Siamak Yassemi

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  1. Pooyan Moradifar
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  2. Siamak Yassemi
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Correspondence to Pooyan Moradifar.

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Presented by: Henning Krause

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Moradifar, P., Yassemi, S. Infinitely Generated Gorenstein Tilting Modules. Algebr Represent Theor 25, 1389–1427 (2022). https://doi.org/10.1007/s10468-021-10072-8

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