Skip to main content
SpringerLink
Log in

On ⌖-supplemented Modules

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Let R be a ring and M a right R-module. M is called ⌖-supplemented if every submodule of M has a supplement that is a direct summand of M, and M is called completely ⌖-supplemented if every direct summand of M is ⌖-supplemented. In this paper various properties of these modules are developed. It is shown that (1) Any finite direct sum of ⌖-supplemented modules is ⌖-supplemented. (2) If M is ⌖-supplemented and (D3) then M is completely ⌖-supplemented.

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. F. W. Anderson and K. R. Fuller, Rings and Categories of Modules, Springer-Verlag (1992).

  2. G. Azumaya, F-semiperfect modules, J. Algebra, 136 (1991), 73–85.

    Google Scholar 

  3. J. Clark and R. Wisbauer, Σ-extending modules, J. Pure Appl. Algebra, 104 (1995), 19–32.

    Google Scholar 

  4. K. R. Goodearl, Ring Theory, Dekker (New York, 1976).

    Google Scholar 

  5. K. R. Goodearl and R. B. Warfield, An Introduction to Noncommutative Noetherian Rings, London Math. Soc. Student Texts 16 Cambridge Univ. Press (Cambridge, 1989).

    Google Scholar 

  6. J. C. McConnel and J. C. Robson, Noncommutative Noetherian Rings, Wiley-Interscience (Chichester, 1987).

    Google Scholar 

  7. S. H. Mohamed and B. J. Müller, Continuous and Discrete Modules, London Math. Soc. LNS 147 Cambridge Univ. Press (Cambridge, 1990).

    Google Scholar 

  8. P. F. Smith, Modules for which every submodule has a unique closure, in Ring Theory (editors, S. K. Jain and S. T. Rizvi), World Sci. (Singapore, 1993), pp. 302–313.

    Google Scholar 

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

    Google Scholar 

  10. W. Xue, Rings with Morita Duality, Springer Lecture Notes in Math. 1523 Springer-Verlag (Berlin, 1992).

    Google Scholar 

  11. J. M. Zelmanowitz, A class of modules with semisimple behavior, in Abelian Groups and Modules (editors A. Facchini and C. Menini), Kluver Acad. Publ. (Dordrecht, 1995), pp. 491–500.

    Google Scholar 

  12. J. M. Zelmanowitz, Representation of rings with faithful polyform modules, Comm. Algebra, 14 (1986), 1141–1169.

    Google Scholar 

  13. H. Zöschinger, Komplementierte Moduln über Dedekindringen, J. Algebra, 29 (1974), 42–56.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Mathematics, Hacettepe University, 06532, Beytepe, Ankara, Turkey

    A. Harmanci & D. Keskįn

  2. Department of Mathematics, University of Glasgow, Glasgow, G12 8QW, Scotland UK

    P. F. Smith

Authors
  1. A. Harmanci
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. D. Keskįn
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. P. F. Smith
    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

Harmanci, A., Keskįn, D. & Smith, P.F. On ⌖-supplemented Modules. Acta Mathematica Hungarica 83, 161–169 (1999). https://doi.org/10.1023/A:1006627906283

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1006627906283

Keywords

Search

Navigation