Clones of entropic algebras with unit
by
Reinhard Pöschel
Technische Universität Dresden, Germany
Coauthors: Dragan Mašulović

We discuss the question for which algebras the clone of term operations is determined by its k-ary invariants (subalgebras of the k-th cartesian power) for fixed k, e.g. for commutative monoids one can choose k=3. As a generalization we show k=3 for entropic algebras with unit. An entropic algebra is an algebra with pairwise commuting operations. Moreover we have Theorem: Every entropic algebra with weakly neutral element is term-equivalent to a commutative monoid.

Date received: April 29, 2008