Skip to main content
SpringerLink
Log in

Weakly regular modules over normal rings

  • Published:
Siberian Mathematical Journal Aims and scope Submit manuscript

Abstract

Under study are some conditions for the weakly regular modules to be closed under direct sums and the rings over which all modules are weakly regular. For an arbitrary right R-module M, we prove that every module in the category σ(M) is weakly regular if and only if each module in σ(M) is either semisimple or contains a nonzero M-injective submodule. We describe the normal rings over which all modules are weakly regular.

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. Kasch F., Modules and Rings [Russian translation], Mir, Moscow (1981).

    MATH  Google Scholar 

  2. Goodearl K. R., Von Neumann Regular Rings, Krieger, Malabar, FL (1991).

    MATH  Google Scholar 

  3. Baccella G., “Exchange property and the natural preorder between simple modules over semi-Artinian rings,” J. Algebra, 253, No. 1, 133–166 (2002).

    Article  MATH  MathSciNet  Google Scholar 

  4. Nastasescu C. and Popescu N., “Anneaux semi-artiniens,” Bull. Soc. Math. France, 96, 357–368 (1968).

    MATH  MathSciNet  Google Scholar 

  5. Wisbauer R., Foundations of Module and Ring Theory, Gordon and Breach, Philadelphia (1991).

    MATH  Google Scholar 

  6. Anderson F. W. and Fuller K. R., Rings and Categories of Modules, Springer-Verlag, New York (1991).

    Google Scholar 

  7. Nickolson W. K., “I-rings,” Trans. Amer. Math. Soc., 207, 361–373 (1975).

    Article  MathSciNet  Google Scholar 

  8. Hamza H., “I 0-rings and I 0-modules,” Okayama Univ., 40, No. 1, 91–97 (1998).

    MathSciNet  Google Scholar 

  9. Faith C., Algebra: Rings, Modules, and Categories. Vol. 2 [Russian translation], Mir, Moscow (1979).

    Google Scholar 

  10. Keskin D. and Lomp C., “On lifting LE-modules,” Vietnam J. Math., 30, No. 2, 167–176 (2002).

    MATH  MathSciNet  Google Scholar 

  11. Hamsher R. M., “Commutative rings over which every module has a maximal submodule,” Proc. Amer. Math. Soc., 18, No. 6, 1133–1137 (1967).

    Article  MATH  MathSciNet  Google Scholar 

  12. Hirano Y., “On rings over which each module has a maximal submodule,” Comm. Algebra, 26, No. 10, 3435–3445 (1998).

    Article  MATH  MathSciNet  Google Scholar 

  13. Dung N. V., Huynh D. V., Smith P. F., and Wisbauer R., Extending Modules, Pitman, London (1994).

    MATH  Google Scholar 

  14. Vanaja N. and Purav V. M., “Characterization of generalized uniserial rings in terms of factor rings,” Comm. Algebra, 20, No. 8, 2253–2270 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  15. Dung N. V. and Smith P. F., “On semiartinian V-modules,” J. Pure Appl. Algebra, 82, No. 1, 27–37 (1992).

    Article  MATH  MathSciNet  Google Scholar 

  16. Baccella G., “Semiartinian V-rings and semiartinian von Neumann regular rings,” J. Algebra, 173, No. 3, 587–612 (1995).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Chebotarev Research Institute of Mathematics and Mechanics, Kazan, Russia

    A. N. Abyzov

Authors
  1. A. N. Abyzov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. N. Abyzov.

Additional information

Original Russian Text Copyright © 2008 Abyzov A. N.

__________

Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 49, No. 4, pp. 721–738, July–August, 2008.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Abyzov, A.N. Weakly regular modules over normal rings. Sib Math J 49, 575–586 (2008). https://doi.org/10.1007/s11202-008-0055-3

Download citation

  • Received:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11202-008-0055-3

Keywords

Search

Navigation