Non-distributive Cancellative Residuated Lattices

  • James A. Cole
Part of the Developments in Mathematics book series (DEVM, volume 7)


Cancellative residuated lattices are a natural generalization of lattice-ordered groups (l-groups) . In studying this variety, several questions have occurred about residuated lattice orders on free monoids and commutative free monoids. One of these questions is whether every residuated lattice order on a (commutative) free monoid is distributive, a fact known about l-groups. We will construct two examples that shows that this is not necessarily the case.


Residuated Lattice Lattice Order Free Monoid Commutative Monoid Cancellative Monoid 
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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • James A. Cole
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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