Volume 7 of the series Developments in Mathematics pp 1956
A Survey of Residuated Lattices
 P. JipsenAffiliated withDepartment of Mathematics, Vanderbilt University
 , C. TsinakisAffiliated withDepartment of Mathematics, Vanderbilt University
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 latticeordered groups, ideal lattices of rings, linear logic and multivalued 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.
 Title
 A Survey of Residuated Lattices
 Book Title
 Ordered Algebraic Structures
 Book Subtitle
 Proceedings of the Gainesville Conference Sponsored by the University of Florida 28th February — 3rd March, 2001
 Pages
 pp 1956
 Copyright
 2002
 DOI
 10.1007/9781475736274_3
 Print ISBN
 9781441952257
 Online ISBN
 9781475736274
 Series Title
 Developments in Mathematics
 Series Volume
 7
 Series ISSN
 13892177
 Publisher
 Springer US
 Copyright Holder
 Springer Science+Business Media Dordrecht
 Additional Links
 Topics
 eBook Packages
 Editors

 Jorge Martínez ^{(2)}
 Editor Affiliations

 2. Department of Mathematics, University of Florida
 Authors

 P. Jipsen ^{(3)}
 C. Tsinakis ^{(3)}
 Author Affiliations

 3. Department of Mathematics, Vanderbilt University, Nashville, TN, 37240, USA
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