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This monograph introduces and explores the notions of a commutator equation and the equationally defined commutator from the perspective of abstract algebraic logic. An account of the commutator operation associated with equational deductive systems is presented, with an emphasis placed on logical aspects of the commutator for equational systems determined by quasivarieties of algebra. The author discusses the general properties of the equationally defined commutator, various centralization relations for relative congruences, the additivity and correspondence properties of the equationally defined commutator and behavior of the equationally defined commutator in finitely generated quasivarieties. Presenting new and original research not yet considered in the mathematical literature, The Equationally Defined Commutator will be of interest to professional algebraists and logicians, as well as graduate students and other researchers interested in problems of modern algebraic logic.
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