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Group-valued modular functions

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Abstract

Modular functions on a lattice (m(x)+m(y)=m(x∪y)+m(x∩y)) live on modular lattices in that they are induced by modular functions on a quotient modular lattice. Those which identify pairs of the distributive inequality live on distributive lattices in the same sense. The structure of all modular functions on a lattice of finite height is determined. The “distance function” derived by Kranz from a modular function is shown to satisfy the triangle inequality.

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Authors and Affiliations

  1. University of Waterloo, Waterloo, Ontario, Canada

    Isidore Fleischer & Tim Traynor

  2. University of Windsor, Windsor, Ontario, Canada

    Isidore Fleischer & Tim Traynor

Authors
  1. Isidore Fleischer
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  2. Tim Traynor
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Fleischer, I., Traynor, T. Group-valued modular functions. Algebra Universalis 14, 287–291 (1982). https://doi.org/10.1007/BF02483932

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  • DOI: https://doi.org/10.1007/BF02483932

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