Finite representation of commutator sequences
Erhard Aichinger, Neboj\v{s}a Mudrinski
TL;DR
This paper introduces finite representations for the infinite sequence of higher commutators in universal algebra, enabling better understanding of algebraic structures through manageable models.
Contribution
It presents a novel method to finitely represent the infinite higher commutator sequences in universal algebra.
Findings
Finite representations of higher commutator sequences are constructed.
These representations facilitate analysis of algebraic properties.
The approach applies to finite algebras for structural insights.
Abstract
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit finite representations of this sequence.
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Taxonomy
TopicsAdvanced Algebra and Logic · semigroups and automata theory · Rings, Modules, and Algebras