Skip to main content
SpringerLink
Log in

Torsion Functors of Local Cohomology Modules

  • Published:
Algebras and Representation Theory Aims and scope Submit manuscript

Abstract

Through a study of torsion functors of local cohomology modules we improve some non-finiteness results on the top non-zero local cohomology modules with respect to an ideal.

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. Aghapournahr, M., Melkersson, L.: Local cohomology and Serre subcategories. J. Algebra 320, 1275–1287 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  2. Asgharzadeh, M., Tousi, M.: A unified approach to local cohomology modules using Serre classes. arXiv:0712.3875v2 [math.AC]

  3. Brodmann, M.P., Sharp, R.Y.: Local cohomology: an algebraic introduction with geometric applications. In: Cambridge Studies in Advanced Mathematics, p. 60. Cambridge University Press, Cambridge (1998)

    Google Scholar 

  4. Delfino, D., Marley, T.: Cofinite modules of local cohomology. J. Pure Appl. Algebra 121(1), 45–52 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Dibaei, M.T., Yassemi, S.: Associated primes and cofiniteness of local cohomology modules. Manuscr. Math. 117, 199–205 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  6. Grothendieck, A.: Cohomologie Locale des Faisceaux Cohérents et Théorèmes de Lefschetz Locaux et Globaux (SGA 2). North-Holland, Amsterdam (1968)

    Google Scholar 

  7. Hartshorne, R.: Cohomological dimension of algeraic varieties. Ann. Math. 88 (1968), 403–450

    Article  MathSciNet  Google Scholar 

  8. Hartshorne, R.: Affine duality and cofiniteness. Invent. Math 9, 145–164 (1970)

    Article  MATH  MathSciNet  Google Scholar 

  9. Hellus, M.: On the associated primes of Matlis duals of local cohomology modules II. arXiv:0906.0642v2 [math.AC]

  10. Khashyarmanesh, K.: On the finiteness properties of extension and torsion functors of local cohomology modules. Proc. Am. Math. Soc. 135, 1319–1327 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  11. Melkersson, L.: Modules cofinite with respect to an ideal. J. Algebra 285, 649–668 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  12. Rotman, J.: An Introduction to Homological Algebra. Academic, London (1979)

    MATH  Google Scholar 

  13. Yoshida, K.-I.: Cofiniteness of local cohomology modules for ideals of dimension one. Nagoya Math. J. 147, 179–191 (1997)

    MATH  MathSciNet  Google Scholar 

  14. Zöschinger, H.: Minimax moduln. J. Algebra 102, 1–32 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  15. Zöschinger, H.: Koatomare moduln. Math. Z. 170, 221–232 (1980)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Faculty of Mathematical Sciences and Computer, Tarbiat Moallem University, Tehran, Iran

    Mohammad T. Dibaei

  2. School of Mathematics, Institute for Research in Fundamental Sciences (IPM), P.O. Box: 19395-5746, Tehran, Iran

    Mohammad T. Dibaei

  3. Payame Noor University (PNU), Tehran, Iran

    Alireza Vahidi

Authors
  1. Mohammad T. Dibaei
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Alireza Vahidi
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Mohammad T. Dibaei.

Additional information

The research of Mohammad T. Dibaei was in part supported by a grant from IPM (No. 88130126).

Rights and permissions

Reprints and permissions

About this article

Cite this article

Dibaei, M.T., Vahidi, A. Torsion Functors of Local Cohomology Modules. Algebr Represent Theor 14, 79–85 (2011). https://doi.org/10.1007/s10468-009-9177-y

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10468-009-9177-y

Keywords

Mathematics Subject Classifications (2000)

Search

Navigation