On the number of Mal'tsev algebras
by
Andrei Bulatov
Computing Laboratory, University of Oxford

We discuss the problem on the number of Mal'tsev algebras up to term (polynomial) equivalence. Two algebras with the same universe are called term (polynomial) equivalent if their clones of term (polynomial) operations are equal. It is known that, up to polynomial equivalence, there are 2 two-element, 14 three-element and countably many four-element Ma'ltsev algebras. We prove that every three-element Mal'tsev algebra is determined, up to term equivalence, by its subalgebras and isomorphisms between subalgebras. Therefore, up to term equivalence there exist 3161 three-element Mal'tsev algebra.

Date received: May 8, 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 # caee-28.