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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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Representing finite lattices as congruence lattices of finite algebras
by
John W. Snow
Concordia University

Call a finite lattice which is isomorphic to the congruence lattice of a finite algebra representable. In A constructive approach to the finite congruence lattice representation problem (Algebra Universalis 43, 2000), we began exploring constructions by which one can make new representable lattices from known representable lattices. In this talk, we will demonstrate how the techniques from that paper can be used to prove the following two theorems.

Theorem 1: Any subdirect product of a finite distributive lattice and a representable lattice is representable.

Theorem 2: Every finite lattice in the variety generated by M3 is representable.

Date received: December 31, 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-39.