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International Conference on Modern Algebra in conjunction with the 17th annual Shanks Lectures
May 21-24, 2002
Vanderbilt University
Nashville, TN, USA

Organizers
Jonathan Farley, Ralph Freese, Matthew Gould, Peter Jipsen, George McNulty, Miklos Maroti, Alexander Ol'shanskii, Steven Tschantz, Constantine Tsinakis, Matthew Valeriote

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Commutative bounded integral residuated lattices
by
Tomasz Kowalski
Japan Advanced Institute of Science and Technology (JAIST)
Coauthors: Hiroakira Ono (JAIST)

The interest in residuated lattices, i.e., algebras that combine a lattice and a residuated monoid has been recently revived. To this revival we would like to contribute a few remarks about commutative bounded integral residuated lattices, by which we understand residuated lattices that are bounded as lattices, and: (1) the bottom and top elements are constants in the type; (2) the unit of the monoid is the top of the lattice; (3) the monoid is commutative.

Varieties of these correspond in a natural way to a class of substructural logics, known by (some) logicians as ``extensions of FLew''. Thus, for want of a better name, we will call our structures FLew-algebras. We will present some facts about the lattice of subvarieties of FLew-algebras.

Date received: December 30, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caig-20.