A Survey of Residuated Lattices
- P. JipsenAffiliated withDepartment of Mathematics, Vanderbilt University
- , C. TsinakisAffiliated withDepartment of Mathematics, Vanderbilt University
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.
- 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
- pp 19-56
- Print ISBN
- Online ISBN
- Series Title
- Developments in Mathematics
- Series Volume
- Series ISSN
- Springer US
- Copyright Holder
- Springer Science+Business Media Dordrecht
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