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Restricted Injective Dimensions over Cohen-Macaulay Rings

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We show that the small and large restricted injective dimensions coincide for Cohen-Macaulay rings of finite Krull dimension. Based on this, and inspired by the recent work of Sather-Wagstaff and Totushek, we suggest a new definition of Cohen-Macaulay Hom injective dimension. We show that the class of Cohen-Macaulay Hom injective modules is the right constituent of a perfect cotorsion pair. Our approach relies on tilting theory, and in particular, on the explicit construction of the tilting module inducing the minimal tilting class recently obtained in (Hrbek et al. 2022).

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Acknowledgements

The first author was supported by the GAČR project 23-05148S and the Academy of Sciences of the Czech Republic (RVO 67985840). This project was partially developed during the visit of the first author to Università degli Studi di Padova, he would like to thank the Dipartimento di Matematica for their hospitality. The visit was partially funded by DFG (Deutsche Forschungsgemeinschaft) through a scientific network on silting theory.

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  1. Giovanna Le Gros

    Present address: Department de Mathemàtiques, Universitat Autònoma de Barcelona, Bellaterra, 08193, Barcelona, Spain

Authors and Affiliations

  1. Institute of Mathematics, Czech Academy of Sciences, Žitná 25, 115 67, Prague, Czech Republic

    Michal Hrbek

  2. Dipartimento di Matematica “Tullio Levi-Civita”, Università degli Studi di Padova, Via Trieste 63, 35121, Padova, Italy

    Giovanna Le Gros

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  1. Michal Hrbek
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Correspondence to Giovanna Le Gros.

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Hrbek, M., Le Gros, G. Restricted Injective Dimensions over Cohen-Macaulay Rings. Algebr Represent Theor (2024). https://doi.org/10.1007/s10468-024-10262-0

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