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Homogeneously Decomposable Modules

In: Études sur les Groupes abéliens / Studies on Abelian Groups

Author

Listed:
  • George Kolettis

    (University of Notre Dame)

Abstract

The well known theorem of Baer-Kulikov-Kaplansky asserts that a direct summand of a completely decomposable torsion-free abeliah group is again completely decomposable. The study of completely decomposable torsion-free abelian groups was initiated by Baer in [1]. One of the results he proved is that direct summands of such a group are completely decomposable whenever the group satisfies a maximum condition. Kulikov [8] proved that every countable direct summand of an arbitrary completely decomposable torsion-free abelian group is completely decomposable, a nontrivial result. By proving that a direct summand of a direct sum of countably generated modules is again a direct sum of countably generated modules, Kaplan sky [7] obtained the complete theorem. An important contribution was also made by Fuchs [5], vko gave an elegant and much shorter proof of Kulikov’s result.

Suggested Citation

  • George Kolettis, 1968. "Homogeneously Decomposable Modules," Springer Books, in: Études sur les Groupes abéliens / Studies on Abelian Groups, chapter 0, pages 223-238, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-46146-0_13
    DOI: 10.1007/978-3-642-46146-0_13
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