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Archiv der Mathematik

, Volume 76, Issue 5, pp 326–337 | Cite as

Characterizing a class of Warfield modules by Ulm submodules and Ulm factors

  • R. Jarisch
  • O. Mutzbauer
  • E. Toubassi

Abstract.

Warfield modules and simply presented modules are considered whose torsion submodule is a direct sum of cyclics. A correspondence between Warfield modules and completely decomposable groups is established by showing that such a mixed module G is Warfield if and only if \(G/p^{\omega }G\) is simply presented and \(p^{\omega }G\) is completely decomposable. We give an example to show that this result cannot be extended to ordinals \(\sigma >\omega \). We also connect with the work of Nunke to characterize modules G whose zeroth Ulm factors are torsion in terms of \(G/p^\sigma G\) simply presented and \(p^\sigma G\) completely decomposable.

Keywords

Mixed Module Decomposable Group Torsion Submodule 
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.

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • R. Jarisch
    • 1
  • O. Mutzbauer
    • 2
  • E. Toubassi
    • 3
  1. 1.Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, GermanyDE
  2. 2.Mathematisches Institut, Universität Würzburg, Am Hubland, 97074 Würzburg, GermanyDE
  3. 3.Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.US

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