Characterizations of Quasi-Splitting Abelian Groups

  • S. V. Joubert
  • H. J. K. Ohlhoff
  • M. J. Schoeman
Part of the Lecture Notes in Mathematics book series (LNM, volume 1006)

Abstract

An abelian group A is called splitting if its torsion subgroup T is a direct summand of A. The weaker notion of quasi-splitting groups was introduced by Walker [7]: A is called quasi-splitting if there exists an integer n ≠ 0 such that nA is contained in some splitting subgroup of A.

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References

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    L. Fuchs Infinite abelian groups, Volume 1. Academic Press 1970.Google Scholar
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    L. Fuchs Infinite abelian groups, Volume 2. Academic Press 1973.Google Scholar
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    F. Loonstra Essential submodules and essential subdirect products. Symp. Mathematica XXII 1974, 85–105.Google Scholar
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    F. Loonstra and M. J. Schoeman On a paper by Mader (to appear).Google Scholar
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    A. Mader On the automorphism group and the endomorphism ring of an abelian group. Ann. Univ. Sc. Budapest Vol. 8 1965, 3–12.Google Scholar
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    M. J. Schoeman Induced endomorphisms and quasi-splitting abelian groups. Research Report UPW 79/9, University of Pretoria 1979, 1–10.Google Scholar
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    C. P. Walker Properties of Ext and quasi-splitting of abelian groups. Acta Math. Acad. Sci. Hunctar vol. 5, 1964, 157–160.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • S. V. Joubert
    • 1
  • H. J. K. Ohlhoff
    • 2
  • M. J. Schoeman
    • 2
  1. 1.School of MathematicsPretoria TechnikonPretoriaRepublic of South Africa
  2. 2.Department of MathematicsUniversity of PretoriaPretoriaRepublic of South Africa

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