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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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Monotone retracts and NUF in finite posets
by
Csaba Szabó
Department of Algebra and Number Theory, Eötvös University, Budapest
Coauthors: Gábor Kun

We introduce a new version of the concept of order varieties, namely, in addition to retracts and product we require that the class of posets should be closed under taking idempotent subalgebras. As an application we prove that the variety generated by an order-primal algebra is congruence modular if and only if every idempotent subalgeba is connected. We do this by developing a technique of dismantling retracts. We give a polynomial time algorithm to decide whether or not a variety generated by an order-primal algebra is congruence modular and we construct a NUF.

Date received: January 4, 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-51.