Ordered Algebraic Structures pp 19-56

Part of the Developments in Mathematics book series (DEVM, volume 7)

A Survey of Residuated Lattices

  • P. Jipsen
  • C. Tsinakis

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.

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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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