Commutators and congruence lattices
by
William A. Lampe
University of Hawaii
Coauthors: Keith A. Kearnes (University of Louisville), Ross Willard (University of Waterloo)

Various commutators have been defined for algebras. If an algebra belongs to a variety having only modular congruence lattices, then all these commutators agree. However, we show that this is far from being the general case by showing that it is possible to construct an algebra in which all these commutators are distinct from each other. Moreover, this can be done in such a way that the algebra can have any prescribed congruence lattice.

It is know that the structure of the congruence lattice of an algebra can have an impact on the Term Condition commutator. In particular, if the congruence lattice satisfies certain structural conditions then the Term Condition commutator is forced to take only the value zero. In contrast, we show that each of the other commutators is independent of the congruence lattice of the algebra.

Date received: June 10, 1999

Copyright © 1999 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 # cadj-04.