The Equationally-Defined Commutator

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Focusing on abstract algebraic logic, this monograph delves into commutator equations and equationally-defined commutators. It presents a thorough examination of the commutator operation linked to equational deductive systems, highlighting its logical implications within quasivarieties of algebras. The author addresses general properties of the equationally-defined commutator, explores centralization relations for relative congruences, and discusses its additivity, correspondence properties, and behavior in finitely generated quasivarieties.