2002 | OriginalPaper | Buchkapitel
A Survey of Residuated Lattices
verfasst von : P. Jipsen, C. Tsinakis
Erschienen in: Ordered Algebraic Structures
Verlag: Springer US
Enthalten in: Professional Book Archive
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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.