Sequences of commutator operations
Erhard Aichinger, Nebojsa Mudrinski
TL;DR
This paper investigates the structure of sequences of higher commutator operations in the congruence lattice of finite algebras with a Mal'cev term, revealing conditions on their quantity and structure.
Contribution
It characterizes the possible sequences of higher commutator operations in finite algebras with a Mal'cev term, establishing bounds and structural conditions.
Findings
Number of such sequences is at most countably infinite.
If infinite, the lattice is the union of two proper subintervals with nonempty intersection.
Properties of higher commutators constrain the sequences' structure.
Abstract
Given the congruence lattice L of a finite algebra A with a Mal'cev term, we look for those sequences of operations on L that are sequences of higher commutator operations of expansions of A. The properties of higher commutators proved so far delimit the number of such sequences: the number is always at most countably infinite; if it is infinite, then L is the union of two proper subintervals with nonempty intersection.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Rings, Modules, and Algebras