Advertisement

Journal of Mathematical Sciences

, Volume 152, Issue 4, pp 469–478 | Cite as

Determination of a class of countable-rank, torsion-free Abelian groups by their endomorphism rings

  • E. A. Blagoveshchenskaya
Article

Abstract

Determination, up to near isomorphism, of countable-rank, block-rigid, local, almost completely decomposable groups of ring type with cyclic regulator quotient by their endomorphism rings in this class has been proved.

Keywords

Endomorphism Ring Ring Type Homogeneous Component Direct Decomposition Canonical Decomposition 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    D. Arnold, Finite Rank Torsion Free Abelian Groups and Rings, Lect. Notes Math., Vol. 931, Springer (1982).Google Scholar
  2. 2.
    E. Blagoveshchenskaya, “Automorphisms of endomorphism rings of a class of almost completely decomposable groups,” Fundam. Prikl. Mat., 10, No. 2, 23–50 (2004).MATHGoogle Scholar
  3. 3.
    E. Blagoveshchenskaya, “Direct decompositions of local almost completely decomposable groups of countable rank,” Chebyshevskiy Sb., 6, No. 4, 26–49 (2005).Google Scholar
  4. 4.
    E. Blagoveshchenskaya, “Dualities between almost completely decomposable groups and decomposable groups and their endomorphism rings,” J. Math. Sci., 131, No. 5, 5948–5961 (2005).MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    E. Blagoveshchenskaya, “Duality of the theory of almost completely decomposable groups and their endomorphism rings,” Nauchno-Techn. Vedomosti SPbGPU, 1, 69–72 (2006).Google Scholar
  6. 6.
    E. Blagoveshchenskaya, “The dual structure of almost completely decomposable groups and their endomorphism rings,” Russ. Math. Surv., 61, No. 2, 347–348 (2006).MATHCrossRefMathSciNetGoogle Scholar
  7. 7.
    E. Blagoveshchenskaya and R. Göbel, “Classification and direct decompositions of some Butler groups of countable rank,” Comm. Algebra, 30, No. 7, 3403–3427 (2002).MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    E. Blagoveshchenskaya, G. Ivanov, and P. Schultz, “The Baer-Kaplansky theorem for almost completely decomposable groups,” Contemp. Math., 273, 85–93 (2001).MathSciNetGoogle Scholar
  9. 9.
    L. Fuchs, Infinite Abelian Groups, Vols. 1, 2, Academic Press (1970, 1973).Google Scholar
  10. 10.
    P. Krylov, A. Mikhalev, and A. Tuganbaev, Endomorphism Rings of Abelian Groups, Kluwer Academic, Dordrecht (2003).MATHGoogle Scholar
  11. 11.
    A. Mader, Almost Completely Decomposable Abelian Groups, Algebra, Logic and Applications, Vol. 13, Gordon and Breach, Amsterdam (1999).Google Scholar

Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  1. 1.Department of MathematicsSt. Petersburg State Technical UniversitySt. PetersburgRussia

Personalised recommendations