Open AccessThe largest higher commutator sequence
Author(s) -
Nebojša Mudrinski
Publication year - 2019
Publication title -
reports on mathematical logic
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.101
H-Index - 6
eISSN - 2084-2589
pISSN - 0137-2904
DOI - 10.4467/20842589rm.19.004.10652
Subject(s) - permutable prime , mathematics , commutator , congruence (geometry) , lattice (music) , congruence relation , pure mathematics , sequence (biology) , variety (cybernetics) , complete lattice , algebra over a field , discrete mathematics , combinatorics , geometry , statistics , physics , universality (dynamical systems) , lie conformal algebra , quantum mechanics , biology , acoustics , genetics
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.