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Weak n-injective and weak n-fat modules

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Abstract

We introduce and study the concepts of weak n-injective and weak n-flat modules in terms of super finitely presented modules whose projective dimension is at most n, which generalize the n-FP-injective and n-flat modules. We show that the class of all weak n-injective R-modules is injectively resolving, whereas that of weak n-flat right R-modules is projectively resolving and the class of weak n-injective (or weak n-flat) modules together with its left (or right) orthogonal class forms a hereditary (or perfect hereditary) cotorsion theory.

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Acknowledgements

The authors would like to thank the referee for the helpful suggestions and valuable comments.

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Authors and Affiliations

  1. National Institute of Technology (NIT), Warangal-506 004, Warangal, TS, India

    Umamaheswaran Arunachalam

  2. Sona College of Technology, Junction Main Road, Salem-636 005, Salem, Tamil Nadu, India

    Saravanan Raja

  3. Periyar University, Palkalai Nagar, Salem-636 011, Salem, Tamil Nadu, India

    Selvaraj Chelliah

  4. Pondicherry University, Chinna Kalapet, Kalapet, Puducherry, Puducherry-605 014, India

    Joseph Kennedy Annadevasahaya Mani

Authors
  1. Umamaheswaran Arunachalam
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  2. Saravanan Raja
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  3. Selvaraj Chelliah
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  4. Joseph Kennedy Annadevasahaya Mani
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Corresponding author

Correspondence to Selvaraj Chelliah.

Additional information

The third author was supported by DST FIST (Letter No: SR/FST/MSI-115/2016 dated 10th November 2017).

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Arunachalam, U., Raja, S., Chelliah, S. et al. Weak n-injective and weak n-fat modules. Czech Math J 72, 913–925 (2022). https://doi.org/10.21136/CMJ.2022.0225-21

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  • DOI: https://doi.org/10.21136/CMJ.2022.0225-21

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