Skip to main content
SpringerLink
Log in

Modules lattice isomorphic to linearly compact modules

  • Published:
Mathematical Notes Aims and scope Submit manuscript

Abstract

We study modules that are lattice isomorphic to linearly compact modules (in the discrete topology). In particular, we establish the equivalence of the following properties of a moduleM: 1)M satisfies the Grothendieck property AB5* and all its submodules are Goldie finite-dimensional; 2)M is lattice isomorphic to a linearly compact module; 3)M is lattice antiisomorphic to a linearly compact module. We show that a linearly compact module cannot be determined in terms of the lattice of its submodules.

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. P. Vámos, “Classical rings,”J. Algebra,34, No. 1, 114–129 (1975).

    MATH  MathSciNet  Google Scholar 

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

    Google Scholar 

  3. T. Takeuchi, “On cofinite-dimensional modules,”Hokkaido Math. J.,5, No. 1, 1–43 (1976)

    MathSciNet  Google Scholar 

  4. G. M. Brodskii, “Dualisms in modules and on the AB5* condition,”Uspekhi Mat. Nauk [Russian Math. Surveys],38, No. 2, 201–202 (1983).

    MATH  MathSciNet  Google Scholar 

  5. P. Fleury, “A note on dualizing Goldie dimension,”Canad. Math. Bull.,17, No. 6, 511–517 (1974).

    MATH  MathSciNet  Google Scholar 

  6. K. Varadarajan, “Dual Goldie dimension,”Comm. Algebra,7, No. 6, 565–610 (1979).

    MATH  MathSciNet  Google Scholar 

  7. K. Varadarajan, “Modules with supplements,”Pacific J. Math.,82, 559–564 (1979).

    MATH  MathSciNet  Google Scholar 

  8. G. M. Brodskii, “Hom functors and structures of submodules,”Trudy Moskov. Mat. Obshch. [Trans. Moscow Math. Soc.],46, 164–186 (1983).

    MATH  MathSciNet  Google Scholar 

  9. V. P. Camillo, “Modules whose quotients have finite Goldie dimension,”Pacific J. Math.,69, No. 2, 337–338 (1977).

    MATH  MathSciNet  Google Scholar 

  10. G. M. Brodskii, “On modules with AB5* condition,” in:XVI All-Union Algebraic Conference, Abstracts of Reports, Part 2 [in Russian], Leningrad (1981), pp. 18–19.

  11. B. Lemonnier, “AB5* et la dualité de Morita,”C. R. Acad. Sci. Ser. A-B.,289, No. 2, A47-A50 (1979).

    MathSciNet  Google Scholar 

  12. W. Brandal, “Commutative rings whose finitely generated modules decompose,” in:Lecture Notes in Math., Vol.723 (1979), pp. 1–116.

    MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Yaroslavl State University, USSR

    G. M. Brodskii

Authors
  1. G. M. Brodskii
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

Translated fromMatematicheskie Zametki, Vol. 59, No. 2, pp. 174–181, February, 1996.

The author wishes to thank A. V. Mikhalev and A. A. Tuganbaev for valuable discussions and remarks.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Brodskii, G.M. Modules lattice isomorphic to linearly compact modules. Math Notes 59, 123–127 (1996). https://doi.org/10.1007/BF02310950

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02310950

Keywords

Search

Navigation