Archiv der Mathematik

, Volume 69, Issue 1, pp 70–74 | Cite as

Extensions of group-valued modular maps

  • Gerd Waldschaks


The first theorem of this paper characterizes modular extensions of a group-valued modular map defined on a Boolean ring as maximal or minimal elements in the collection of all supermodular or submodular extensions, respectively. Using Zorn's lemma, we obtain results on the existence of a modular majorant or minorant of a supermodular or submodular map, respectively. The results are specialized to positive (super-)modular maps. The final remark includes an economic game theory application.


Game Theory Final Remark Minimal Element Theory Application Boolean Ring 


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Copyright information

© Birkhäuser Verlag, Basel 1997

Authors and Affiliations

  • Gerd Waldschaks
    • 1
  1. 1.Bodelschwinghstraße 11, D-67105 Schifferstadt, GermanyDE

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