A relational description of higher commutators in Malćev varieties

Abstract

We give a relational description of higher commutator operators, which were introduced by Bulatov, in varieties with a Mal'cev term. Furthermore, we use this result to prove that for every algebra with a Mal'cev term, there exists a largest clone containing the Mal'cev operation and having the same congruence lattice and the same higher commutator operators as the original algebra.

We also give a local variant of this theorem.

Keywords

• relational
• description
• higher
• commutators
• Malćev
• varieties