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The Recollements of Abelian Categories: Cotorsion Dimensions and Cotorsion Triples

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Abstract

In this paper, we study the cotorsion dimensions and cotorsion triples in the recollements of abelian categories. The main results are that recollements induce new (resp. complete hereditary) cotorsion triples from the middle category and that the cotorsion dimensions are bounded under certain conditions. As an application, the cotorsion triples in the recollements of module categories with respect to triangular matrix algebras are recovered.

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Acknowledgements

The authors thank the referee for his/her useful comments. This work was supported by National Natural Science Foundation of China (Grant No. 11671126) and Natural Science Foundation of Shandong Province (Grant No. ZR2020QA002).

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Authors and Affiliations

  1. College of Mathematics and Statistics, Heze University, Shandong, 274015, People’s Republic of China

    Xuerong Fu

  2. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Yonggang Hu

  3. Département de mathématiques, Université de Sherbrooke, Sherbrooke, Québec, J1K 2R1, Canada

    Yonggang Hu

Authors
  1. Xuerong Fu
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  2. Yonggang Hu
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Correspondence to Xuerong Fu.

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Communicated by Santiago Zarzuela.

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Fu, X., Hu, Y. The Recollements of Abelian Categories: Cotorsion Dimensions and Cotorsion Triples. Bull. Iran. Math. Soc. 48, 963–977 (2022). https://doi.org/10.1007/s41980-021-00557-z

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  • DOI: https://doi.org/10.1007/s41980-021-00557-z

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