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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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Continuum many idempotent minimal residuated-lattice varieties
by
Nikolaos Galatos
Vanderbilt University

A residuated lattice is an algebra L = < L, /\ , \/ , ·, e, / , \ > , such that < L, /\ , \/ > is lattice, < L, ·, e > is monoid and for all a, b, c in L,   ab <= c iff a <= c / b iff b <= a \ c. Residuated lattices form a variety, which is denoded by RL. We investigate the bottom of the subvariety lattice of RL and prove that there are continuum many atoms that satisfy the identity x2 = x.

Date received: March 26, 2002

Copyright © 2002 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-89.