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arXiv · 1412.5776

A relational description of higher commutators in Mal'cev varieties

Jakub Opršal
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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.

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Jakub Opršal. 2018-07-10. A relational description of higher commutators in Mal'cev varieties. https://doi.org/10.1007/s00012-016-0391-2

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