Skip to main content
SpringerLink
Log in

\({\mathcal {I}}\)-lifting modules and noncosingularity

  • Published:
ANNALI DELL'UNIVERSITA' DI FERRARA Aims and scope Submit manuscript

Abstract

By using the concept of non-cosingularity, we introduced the class of \(\gamma \)-\({\mathcal {I}}\)-lifting modules which is a generalization of \({\mathcal {I}}\)-lifting modules. Also we investigate \(\gamma \)-\({\mathcal {I}}\)-lifting and seek at the question that when \(\gamma \)-\({\mathcal {I}}\)-lifting is preserved by finite direct sums.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Clark, J., Lomp, C., Vanaja, N., Wisbauer, R.: Lifting modules -supplements and projectivity in module theory. Front. Math. Birkhauser (2006)

  2. Lee, G., Rizvi, S.T., Roman, C.S.: Dual Rickart modules. Comm. Algebra 39, 4036–4058 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  3. Amouzegar, K.T.: A generalization of lifting modules. Ukr. Math. J. 66(11), 1654–1664 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  4. Talebi, Y., Vanaja, N.: The torsion theory cogenerated by \(M\)-small modules. Comm. Algebra 30(3), 1449–1460 (2002)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hosseinpour, M., Hamzekolaee, A.R.M.: \(\gamma \) -small submodules and \(\gamma \) -lifting modules. East-West J. Math. 22(1), 52–63 (2020)

    MathSciNet  MATH  Google Scholar 

  6. Hamzekolaee, A.R.M.: An approach to \(H\)-supplemented via noncosingular modules. Annali Dell Universita Di Ferrera 67, 111–120 (2021)

    Article  MathSciNet  MATH  Google Scholar 

  7. Amouzegar, T., Keskin, D., Talebi, Y.: \(t\)-dual Baer modules and \(t\)-lifting modules. Vietnam J. Math. 42, 159–169 (2014)

    Article  MathSciNet  MATH  Google Scholar 

  8. Keskin, D.: Finite direct sums of \(D_1\)-modules. Turk. J. Math. 22, 85–91 (1998)

    MATH  Google Scholar 

  9. Ghorbani, A., Vedadi, M.R.: Epi-retractable modules and some applications. Bull. Iran. Math. Soc. 35(1), 155–166 (2009)

    MathSciNet  MATH  Google Scholar 

  10. Amouzegar, T.: Hamzekolaee, ARM: Lifting modules with respect to image of a fully invariant submodule. Novi Sad J. Math. 20(2), 41–50 (2020)

    MathSciNet  MATH  Google Scholar 

  11. Tribak, R., Talebi, Y., Hamzekolaee, A.R.M., Asgari, S.: \(\oplus \)-supplemented modules relative to an ideal. Haccetepe J. Math. Stat. 45(1), 107–120 (2016)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Pure Mathematics, Faculty of Mathematical Sciences, University of Mazandaran, Babolsar, Iran

    A. R. Moniri Hamzekolaee

  2. Department of Mathematics, Quchan University of Technology, P.O.Box 94771-67335, Quchan, Iran

    T. Amouzegar

Authors
  1. A. R. Moniri Hamzekolaee
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. T. Amouzegar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to T. Amouzegar.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Springer Nature or its licensor holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Moniri Hamzekolaee, A.R., Amouzegar, T. \({\mathcal {I}}\)-lifting modules and noncosingularity. Ann Univ Ferrara 69, 363–374 (2023). https://doi.org/10.1007/s11565-022-00432-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11565-022-00432-7

Keywords

Mathematics Subject Classification

Search

Navigation