Skip to main content
SpringerLink
Log in

Cotorsion pairs associated with Auslander categories

  • Published:
Israel Journal of Mathematics Aims and scope Submit manuscript

Abstract

We prove that the Auslander category determined by a semidualizing module is the left half of a perfect cotorsion pair. We also prove that the Bass class determined by a semidualizing module is preenveloping.

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. L. L. Avramov and H.-B. Foxby, Ring homomorphisms and finite Gorenstein dimension, Proceedings of the London Mathematical Society. Third Series 75 (1997), 241–270.

    Article  MATH  MathSciNet  Google Scholar 

  2. L. Bican, R. El Bashir and E. E. Enochs, All modules have flat covers, Bulletin London Mathematical Society 33 (2001), 385–390.

    Article  MATH  Google Scholar 

  3. L. W. Christensen, Semi-dualizing complexes and their Auslander categories, Transactions of the American Mathematical Society 353 (2001), 1839–1883 (electronic).

    Article  MATH  MathSciNet  Google Scholar 

  4. L. W. Christensen, A. Frankild and H. Holm, On Gorenstein projective, injective and flat dimensions — a functorial description with applications, Journal of Algebra 302 (2006), 231–279.

    Article  MATH  MathSciNet  Google Scholar 

  5. L. W. Christensen and H. Holm, Ascent properties of Auslander categories, Canadian Journal of Mathematics 61 (2009), 76–108.

    Article  MATH  MathSciNet  Google Scholar 

  6. B. Eckmann and A. Schopf, Über injektive Moduln, Archiv der Mathematik 4 (1953), 75–78.

    Article  MATH  MathSciNet  Google Scholar 

  7. E. E. Enochs and O. M. G. Jenda, Relative Homological Algebra, de Gruyter Expositions in Mathematics, Vol. 30, Walter de Gruyter & Co., Berlin, 2000.

    MATH  Google Scholar 

  8. E. E. Enochs, O. M. G. Jenda and J. Xu, Foxby duality and Gorenstein injective and projective modules, Transactions of the American Mathematical Society 348 (1996), 3223–3234.

    Article  MATH  MathSciNet  Google Scholar 

  9. E. E. Enochs and J. A. López-Ramos, Kaplansky classes, Rendiconti del Seminario Matematico della Universitá di Padova 107 (2002), 67–79.

    MATH  Google Scholar 

  10. E. E. Enochs and S. Yassemi, Foxby equivalence and cotorsion theories relative to semidualizing modules, Mathematica Scandinavica 95 (2004), 33–43.

    MATH  MathSciNet  Google Scholar 

  11. H.-B. Foxby, Gorenstein modules and related modules, Mathematica Scandinavica 31 (1972), 267–284.

    MathSciNet  Google Scholar 

  12. A. Frankild and S. Sather-Wagstaff, The set of semidualizing complexes is a nontrivial metric space, Journal of Algebra 308 (2007), 124–143.

    Article  MATH  MathSciNet  Google Scholar 

  13. E. S. Golod, G-dimension and generalized perfect ideals, Trudy Matematicheskogo Instituta Imeni V. A. Steklova 165 (1984), 62–66, Algebraic geometry and its applications.

    MATH  MathSciNet  Google Scholar 

  14. H. Holm and P. Jørgensen, Semi-dualizing modules and related Gorenstein homological dimensions, Journal of Pure and Applied Algebra 205 (2006), 423–445.

    Article  MATH  MathSciNet  Google Scholar 

  15. H. Holm and D. White, Foxby equivalence over associative rings, Journal of Mathematics of Kyoto University 47 (2007), 781–808.

    MATH  MathSciNet  Google Scholar 

  16. S. Iyengar and S. Sather-Wagstaff, G-dimension over local homomorphisms. Applications to the Frobenius endomorphism, Illinois Journal of Mathematics 48 (2004), 241–272.

    MATH  MathSciNet  Google Scholar 

  17. S. Sather-Wagstaff, Semidualizing modules and the divisor class group, Illinois Journal of Mathematics (to appear), available from the ArXiv /math.AC/0408399

  18. W. V. Vasconcelos, Divisor Theory in Module Categories, North-Holland Mathematics Studies, Vol. 14, North-Holland Publ. Co., Amsterdam, 1974.

    MATH  Google Scholar 

  19. J. Xu, Flat Covers of Modules, Lecture Notes in Mathematics, Vol. 1634, Springer-Verlag, Berlin, 1996.

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, University of Kentucky, Lexington, KY, 40506-0027, USA

    Edgar E. Enochs

  2. Department of Natural Sciences, Faculty of Life Sciences, University of Copenhagen, Thorvaldsensvej 40, 6th floor, 1871, Frederiksberg C, Denmark

    Henrik Holm

Authors
  1. Edgar E. Enochs
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Henrik Holm
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Enochs, E.E., Holm, H. Cotorsion pairs associated with Auslander categories. Isr. J. Math. 174, 253–268 (2009). https://doi.org/10.1007/s11856-009-0113-y

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11856-009-0113-y

Keywords

Search

Navigation