A relational description of higher commutators in Mal'cev 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 on the same underlying set containing the Mal'cev operation and having the same congruence lattice and the same higher commutator operators as the original algebra. A local variant of this theorem is given.

Cited by in corpus (3)

• Complexity of term representations of finitary functions
• Generating subdirect products
• Congruence preserving expansions of nilpotent algebras