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A Survey of Residuated Lattices

  • P. Jipsen
  • C. Tsinakis
Part of the Developments in Mathematics book series (DEVM, volume 7)

Abstract

Residuation is a fundamental concept of ordered structures and categories. In this survey we consider the consequences of adding a residuated monoid operation to lattices. The resulting residuated lattices have been studied in several branches of mathematics, including the areas of lattice-ordered groups, ideal lattices of rings, linear logic and multi-valued logic. Our exposition aims to cover basic results and current developments, concentrating on the algebraic structure, the lattice of varieties, and decidability.

We end with a list of open problems that we hope will stimulate further research.

Keywords

Word Problem Residuated Lattice Modular Lattice Equational Basis Gentzen System 
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

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • P. Jipsen
    • 1
  • C. Tsinakis
    • 1
  1. 1.Department of MathematicsVanderbilt UniversityNashvilleUSA

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