The finite quasi-equational base problem
by
Miklós Maróti
Vanderbilt University, Nashville, TN, USA
Coauthors: J. Jezek, R. McKenzie

It is expected that the finite quasi-equational base problem, whether a finite algebra possesses a finite basis for its quasi-equations, is undecidable. This problem is similar to Tarski's finite equational base problem, which was proved by Ralph McKenzie. In his proof flat digraph algebras played a significant role, which prompted us to study their quasi-equational theories.

We prove that finite flat digraph algebras and, more generally, finite compatible flat algebras satisfying a certain condition are finitely q-based (possess a finite basis for their quasi-equations). We also exhibit an example of a twelve-element compatible flat algebra that is not finitely q-based.

Date received: July 17, 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 # caiv-52.