Skip to main content
SpringerLink
Log in

On the Quasi-Endomorphism Rings of Quasi-Decomposable Torsion-Free Abelian Groups of Rank 4 with a Strongly Indecomposable Quasi-Summand of Rank 2

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

Abstract

We obtain a description of quasi-endomorphism rings of torsion-free Abelian groups G of rank 4 that are quasi-decomposable into a direct sum of groups A1 and A2 of rank 1 and a strongly indecomposable group B of rank 2 in the case where the quasi-homomorphism group ℚ ⨂ Hom(B,A2) has rank 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. D. M. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., Vol. 931, Springer, Berlin (1982).

  2. R. A. Beaumont and R. S. Pierce, “Torsion free groups of rank two,” Mem. Am. Math. Soc., 38, 1–41 (1961).

    MathSciNet  MATH  Google Scholar 

  3. A. V. Cherednikova, “Quasi-endomorphism rings of almost completely decomposable torsion-free Abelian groups of rank 3,” in: Abelian Groups and Modules, Vol. 13-14, Tomsk. Univ., Tomsk (1996), pp. 237–242.

  4. A. V. Cherednikova, “Quasi-endomorphism rings of quasi-decomposable torsion-free Abelian groups of rank 3,” in: Abelian Groups and Modules, Vol. 13-14, Tomsk. Univ., Tomsk (1996), pp. 224–236.

  5. A. A. Fomin, “Abelian groups with a τ -adic relation,” Algebra Logika, 28, No. 1, 83–104 (1989).

  6. L. Fuchs, Infinite Abelian Groups, Vol. 2, Academic Press, New York (1973).

    MATH  Google Scholar 

  7. R. S. Pierce, Associative Algebras, Springer, Berlin (1982).

    Book  MATH  Google Scholar 

  8. J. K. Reid, “On the rings of quasi-endomorphism of torsion-free Abelian groups,” Topics in Abelian Groups, Scott, Foresman, Chicago (1963), pp. 51–68.

  9. R. Warfield, “Homomorphisms and duality for torsion free groups,” Math. Z., 107, 189–200 (1968).

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Kostroma State Technological University, ul. Gerjinsky, 17, Kostroma, 156005, Russia

    A. V. Cherednikova

Authors
  1. A. V. Cherednikova
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to A. V. Cherednikova.

Additional information

Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 20, No. 5, pp. 209–225, 2015.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cherednikova, A.V. On the Quasi-Endomorphism Rings of Quasi-Decomposable Torsion-Free Abelian Groups of Rank 4 with a Strongly Indecomposable Quasi-Summand of Rank 2. J Math Sci 230, 491–501 (2018). https://doi.org/10.1007/s10958-018-3757-5

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10958-018-3757-5

Search

Navigation