Non-distributive Cancellative Residuated Lattices

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

Abstract

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.

Keywords

Residuated Lattice Lattice Order Free Monoid Commutative Monoid Cancellative Monoid 
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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References

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    M. Anderson and T. Feil, Lattice-Ordered Groups: an introduction. (1988) D. Reidel Publishing Company.MATHCrossRefGoogle Scholar
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    K. Blount and C. Tsinakis, The structure of Residuated Lattices. Preprint.Google Scholar
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    P. Jipsen and C. Tsinakis, A Survey of Residuated Lattices. (2002) In these Proceedings, 19–56.Google Scholar
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    P. Bahls, J. Cole, P. Jipsen, N. Galatos, and C. Tsinakis, Cancellative Residuated Lattices. Preprint.Google Scholar

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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