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On the subcategories of n-torsionfree modules and related modules

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Abstract

Let R be a commutative noetherian ring. Denote by \({\textsf{mod }}\,R\) the category of finitely generated R-modules. In this paper, we study n-torsionfree modules in the sense of Auslander and Bridger, by comparing them with n-syzygy modules, and modules satisfying Serre’s condition \((\mathrm {S}_n)\). We mainly investigate closedness properties of the full subcategories of \({\textsf{mod }}\,R\) consisting of those modules.

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Acknowledgements

The authors thank the anonymous referee for reading the paper carefully and giving them helpful comments.

Funding

Ryo Takahashi was partly supported by JSPS Grant-in-Aid for Scientific Research 19K03443.

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Authors and Affiliations

  1. Department of Mathematics, University of Kansas, 1460 Jayhawk Blvd., Lawrence, KS, 66045, USA

    Souvik Dey

  2. Graduate School of Mathematics, Nagoya University, Furocho, Chikusaku, Nagoya, 464-8602, Japan

    Ryo Takahashi

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  1. Souvik Dey
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  2. Ryo Takahashi
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Correspondence to Ryo Takahashi.

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Dey, S., Takahashi, R. On the subcategories of n-torsionfree modules and related modules. Collect. Math. 74, 113–132 (2023). https://doi.org/10.1007/s13348-021-00338-1

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  • DOI: https://doi.org/10.1007/s13348-021-00338-1

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