Skip to main content
SpringerLink
Log in

Relative T-injective modules and relative T-flat modules

  • Published:
Chinese Annals of Mathematics, Series B Aims and scope Submit manuscript

Abstract

Let T be a Wakamatsu tilting module. A module M is called (n, T)-copure injective (resp. (n, T)-copure flat) if ɛ 1 T (N, M) = 0 (resp. Γ T1 (N, M) = 0) for any module N with T-injective dimension at most n (see Definition 2.2). In this paper, it is shown that M is (n, T)-copure injective if and only if M is the kernel of an I n (T)-precover f: A → B with A ∈ Prod T. Also, some results on Prod T-syzygies are presented. For instance, it is shown that every nth Prod T-syzygy of every module, generated by T, is (n, T)-copure injective.

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. Angleri-Hugel, L. and Coelho, F. U., Infinitely generated tilting modules of finite projective dimension, Forum Math., 13, 2001, 239–250.

    Article  MathSciNet  Google Scholar 

  2. Bazzoni, S., A characterization of n-cotilting and n-tilting modules, J. Algebra, 273, 2005, 359–372.

    Article  MathSciNet  Google Scholar 

  3. Enochs, E. E. and Jenda, O. M. G., Relative Homological Algebra, Walter de Gruyter, Berlin, New York, 2000.

    Book  MATH  Google Scholar 

  4. Green, E. L., Reiten, I. and Solberg, O., Dualities on Generalized Koszul Algebras, Mem. Amer. Math. Soc., 159, A. M. S., Providence, RI, 2002, 754.

    Google Scholar 

  5. Nikmehr, M. J., Shaveisi, F. and Nikandish, R., n-Projective modules, Algebras Groups Geom., 24, 2007, 447–454.

    MATH  MathSciNet  Google Scholar 

  6. Nikmehr, M. J. and Shaveisi, F., T-Dimension and (n + 1/2, T)-projective modules, Southeast Asian Bull. Math., 35, 2011, 1–11.

    Google Scholar 

  7. Rotman, J. J., An Introduction to Homological Algebra, Academic Press, New York, 1979.

    MATH  Google Scholar 

  8. Wakamatsu, T., On modules with trivial self-extension, J. Algebra, 114, 1998, 106–114.

    Article  MathSciNet  Google Scholar 

  9. Wei, J., n-Star modules and n-tilting modules, J. Algebra, 283, 2005, 711–722.

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Faculty of Science, K. N. Toosi University of Technology, Tehran, Iran

    Mohammad Javad Nikmehr

  2. Department of Mathematics, Razi University, Kermanshah, Iran

    Farzad Shaveisi

Authors
  1. Mohammad Javad Nikmehr
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Farzad Shaveisi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad Javad Nikmehr.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikmehr, M.J., Shaveisi, F. Relative T-injective modules and relative T-flat modules. Chin. Ann. Math. Ser. B 32, 497–506 (2011). https://doi.org/10.1007/s11401-011-0662-3

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11401-011-0662-3

Keywords

2010 MR Subject Classification

Search

Navigation