Advertisement

Journal of Mathematical Sciences

, Volume 197, Issue 5, pp 649–654 | Cite as

Determination of the Direct Sums of Rational Groups by H-Representations of the Endomorphism Rings up to Equality

  • E. N. Kurmanova
  • A. M. Sebeldin
Article
  • 27 Downloads

Abstract

The problem of determination of Abelian groups (up to isomorphism) by their rings of endomorphisms in the class of completely decomposable torsion-free Abelian groups has been solved earlier. For the class of direct sums of rational groups, one can speak of determination of Abelian groups by rational representations of their endomorphism rings up to equality. In this paper, we consider this problem for the class of finite direct sums of rational groups and for some subclasses.

Keywords

Abelian Group Prime Number Rational Number Rational Group Rational Matrice 
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.
    P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Abelian Groups and Their Endomorphism Rings [in Russian], Factorial, Moscow (2006).Google Scholar
  2. 2.
    E. N. Kurmanova and A. M. Sebeldin, “Necessary and sufficient conditions for Hom-divisibility of rational groups,” Izv. Vyssh. Uchebn. Zaved., Mat., No. 8 (531), 38–41.Google Scholar
  3. 3.
    A. M. Sebeldin, “The conditions of isomorphism of completely decomposable torsion-free Abelian groups with isomorphic endomorphism rings,” Mat. Zametki, 11, No. 4, 403–408.Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.State Pedagogical University of Nizhny NovgorodNizhny NovgorodRussia

Personalised recommendations