Skip to main content
SpringerLink
Log in

Warfield’s Duality and Malcev’s Matrix

  • Published:
Journal of Mathematical Sciences Aims and scope Submit manuscript

Abstract

In this work, we investigate relations between Malcev’s matrices of a torsion-free group G of finite rank and Malcev’s matrices of groups Hom(R,G) and Hom(G,R), where G is a locally free group and R is a torsion-free group of rank 1.

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. D. M. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., V. 931, Springer, Berlin (1982).

  2. D. Derry, “Über eine Klasse von Abelschen Gruppen,” Proc. London Math. Soc., 43, 490–506 (1938).

    Article  MathSciNet  Google Scholar 

  3. A. A. Fomin, “Invariants for Abelian groups and dual exact sequences,” J. Algebra, 322, 2544–2565 (2009).

    Article  MATH  MathSciNet  Google Scholar 

  4. L. Fuchs, Infinite Abelian Groups, Academic Press, New York (1970, 1973).

  5. A. G. Kurosh, “Primitive torsionfreie abelsche Gruppen vom endlichen Range,” Ann. Math., 38, 175–203 (1937).

    Article  MATH  MathSciNet  Google Scholar 

  6. A. G. Kurosh, Theory of Groups [in Russian], Moscow (1967).

  7. A. I. Malcev, “Torsion-free Abelian group of finite rank,” Math. J., 4, 45–68 (1938).

    MATH  Google Scholar 

  8. R. B. Warfield, Jr., “Homomorphisms and duality for Abelian groups,” Math. Z., 107, 189–212 (1968).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Moscow Pedagogical State University, Moscow, Russia

    J. V. Kostromina

Authors
  1. J. V. Kostromina
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to J. V. Kostromina.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 17, No. 8, pp. 77–94, 2011/12.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Kostromina, J.V. Warfield’s Duality and Malcev’s Matrix. J Math Sci 197, 635–648 (2014). https://doi.org/10.1007/s10958-014-1746-x

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-014-1746-x

Keywords

Search

Navigation