The Largest Higher Commutator Sequence

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...

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Bibliographic Details
Published in:Reports on mathematical logic 2019, Vol.54 (54), p.83-94
Main Author: Mudrinski, Nebojša
Format: Article
Language:English
Subjects:
Analytic Philosophy
Commutators
Finite element analysis
Lattice theory
Logic
Mathematics
Sequences
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Summary: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.
ISSN:0137-2904
2084-2589
DOI:10.4467/20842589RM.19.004.10652