The largest higher commutator sequence

Nebojša Mudrinski

Abstrakt

Given the congruence lattice L of a finite algebra A that generates a congruence permutable variety, we  look for those sequences of operations on L that have the properties of higher commutator operations of expansions of A. If we introduce the order of such sequences in the natural way the question is whether exists or not the largest one. The answer is positive. We provide a description of the largest element and as a consequence we obtain that the sequences form a complete lattice.

AMS subject classification: Primary 06B10; Secondary 06A07, 08A40.

Słowa kluczowe: lattices, sequences of operations, commutators
References

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[12] N. Mudrinski, On Polynomials in Mal’cev Algebras, Ph.D. thesis, University of Novi Sad, 2009. Available at: http://people.dmi.uns.ac.rs/˜nmudrinski/DissertationMudrinski.pdf.

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