Skip to main content
SpringerLink
Log in

Modules Which Satisfy the Radical Formula

  • Published:
Acta Mathematica Hungarica Aims and scope Submit manuscript

Abstract

Let \(R\) be a commutative ring. Then an \(R\)-module M satisfies the radical formula when \(M = M_1 \oplus M_2 \) is a direct sum of a submodule M 1 which satisfies the radical formula and a semi-artinian submodule M 2.

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 (Berlin, 1974).

    Google Scholar 

  2. Nguyen Viet Dung and P. F. Smith, On semi-artinian V-modules, J. Pure Appl. Algebra, 82 (1992), 27-37.

    Google Scholar 

  3. J. Jenkins and P. F. Smith, On the prime radical of a module over a commutative ring, Comm. Algebra, 20 (1992), 3593-3602.

    Google Scholar 

  4. Ka Hin Leung and Shing Hing Man, On commutative Noetherian rings which satisfy the radical formula, Glasgow Math. J., 39 (1997), 285-293.

    Google Scholar 

  5. R. L. McCasland and M. E. Moore, On radicals of submodules, Comm. Algebra, 19 (1991), 1327-1341.

    Google Scholar 

  6. R. L. McCasland and P. F. Smith, Prime submodules of Noetherian modules, Rocky Mtn. J., 23 (1993), 1041-1062.

    Google Scholar 

  7. D. S. Passman, The Algebraic Structure of Group Rings, Wiley-Interscience (New York, 1977).

    Google Scholar 

  8. D. Pusat-Yilmaz and P. F. Smith, Radicals of submodules of free modules, Comm. Algebra, 27 (1999), 2253-2266.

    Google Scholar 

  9. H. Sharif, Y. Sharifi and S. Namazi, Rings satisfying the radical formula, Acta Math. Hungar., 71 (1996), 103-108.

    Google Scholar 

  10. D. W. Sharpe and P. Vamos, Injective Modules, Cambridge University Press (Cambridge, 1972).

    Google Scholar 

  11. B. Stenström, Rings of Quotients, Springer-Verlag (Berlin, 1975).

    Google Scholar 

  12. O. Zariski and P. Samuel, Commutative Algebra, Volume I, Van Nostrand (Princeton, 1958).

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department Of Mathematics, Abant Izzet Baysal University, 14280, Bolu, Turkey

    Dilel Pusat-Yilmaz

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

    Patrick F. Smith

Authors
  1. Dilel Pusat-Yilmaz
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Patrick 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

Pusat-Yilmaz, D., Smith, P.F. Modules Which Satisfy the Radical Formula. Acta Mathematica Hungarica 95, 155–167 (2002). https://doi.org/10.1023/A:1015624503160

Download citation

  • Issue Date:

  • DOI: https://doi.org/10.1023/A:1015624503160

Search

Navigation