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Journal of Mathematical Sciences

, Volume 197, Issue 5, pp 623–624 | Cite as

Some Classes of Hopfian Abelian Groups

  • E. V. Kaygorodov
Article
  • 27 Downloads

Abstract

This paper describes the Hopfian groups in some classes of Abelian groups. A complete description of Hopfian divisible groups is presented; on the basis of this description, the study of Hopficity of arbitrary Abelian groups is reduced to the study of Hopficity of reduced groups. Direct sums of cyclic groups that are Hopfian groups are characterized. Finally, the paper looks at specific examples of rings whose additive groups are Hopfian.

Keywords

Abelian Group Cyclic Group Additive Group Commutative Ring Algebraic System 
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.

References

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    E. V. Kaygorodov, “About Hopficity of additive groups of some rings,” in: Modern Problems of Mathematics and Mechanics, Proc. Third National Youth Conf., Tomsk (2012), pp. 19–22.Google Scholar
  2. 2.
    E. V. Kaygorodov, “Hopfian Abelian groups,” Tomsk State Univ. J. Math. Mech., No. 2 (18), 5–12 (2012).Google Scholar
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    P. A. Krylov, A. V. Mikhalev, and A. A. Tuganbaev, Endomorphism Rings of Abelian Groups [in Russian], Faktorial, Moscow (2006).Google Scholar
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    P. A. Krylov, A. A. Tuganbaev, and A. R. Chekhlov, Exercises on the Theory of Groups, Rings and Fields [in Russian], Tomsk. Gos. Univ., Tomsk (2008).Google Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Tomsk State UniversityTomskRussia

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