On FI-t-lifting modules

Abstract

In this paper, we introduce the notion of FI-t-lifting modules which is a proper generalization of both the concepts of t-lifting modules and FI-lifting modules. We show that a direct sum of FI-t-lifting modules is not FI-t-lifting, in general. It is also shown that if M is an FI-t-lifting module, then \({\overline{Z}}^2(M)\) is a direct summand of M and \({\overline{Z}}^2(M)\) is a noncosingular FI-lifting module. The last part of the paper is devoted to the study of amply supplemented FI-t-lifting modules.

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Acknowledgements

The authors are very grateful to the referees for their valuable suggestions and comments which improved this paper.

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Correspondence to Rachid Tribak.

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Tribak, R., Talebi, Y., Hosseinpour, M. et al. On FI-t-lifting modules. Bol. Soc. Mat. Mex. 26, 973–989 (2020). https://doi.org/10.1007/s40590-020-00301-3

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Keywords

  • FI-lifting modules
  • FI-t-lifting modules
  • t-Lifting modules
  • t-Small submodules

Mathematics Subject Classification

  • 16D10
  • 16D80