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Archiv der Mathematik

, Volume 71, Issue 5, pp 349–357 | Cite as

Characterizing a class of simply presented modules by relation arrays

  • Ralf Jarisch
  • Otto Mutzbauer
  • Elias Toubassi

Abstract.

Simply presented modules and Warfield modules are described in a class of mixed modules \(\cal H \) with the property that the torsion submodule is a direct sum of cyclics and the quotient modulo the torsion submodule is divisible of arbitrary rank. Analogous to a result of Warfield it is shown that the mixed modules of torsion-free rank one are in some sense the building blocks of such modules. The results extend our previous work describing this class by relation arrays which are a natural outgrowth of their basic generating systems. Moreover, an intimate connection is shown between relation arrays and the indicators of modules. Furthermore, we prove two realizability results one of which is analogous to a theorem of Megibben for mixed modules of torsion-free rank one. One gives necessary and sufficient conditions on when a relation array of a module can realize an indicator of finite-type while the other shows that an admissable indicator can be realized by a simply presented module of torsion-free rank one.

Keywords

Building Block Generate System Mixed Module Basic Generate Realizability Result 
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 1998

Authors and Affiliations

  • Ralf Jarisch
    • 1
  • Otto Mutzbauer
    • 1
  • Elias Toubassi
    • 2
  1. 1.Mathematisches Institut, Universität Würzburg, Am Hubland, D-97074 Würzburg, GermanyDE
  2. 2.Department of Mathematics, University of Arizona, Tucson, Arizona 85721, U.S.A.US

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