Commutators and compatible operations
by
A. Szendrei
University of Louisville

Starting from J. D. H. Smith's definition of centrality, M. C. Pedicchio and G. Janelidze developed a categorical definition of a commutator which they showed to coincide with the usual commutator in congruence modular varieties. An algebra in a variety V is abelian with respect to this commutator if and only if it can be embedded in an affine group object in V. Equivalently, A is abelian in V if and only if A can be embedded in an algebra A' in V that has a compatible group Mal'tsev operation xy^-1z. We will discuss the relationship between this commutator and some commutators defined by term conditions.

Date received: May 19, 2000

Copyright © 2000 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 # cafg-08.