The Equationally-Defined Commutator

A Study in Equational Logic and Algebra

  • Janusz Czelakowski

Table of contents

  1. Front Matter
    Pages i-ix
  2. Janusz Czelakowski
    Pages 1-6
  3. Janusz Czelakowski
    Pages 7-26
  4. Janusz Czelakowski
    Pages 65-97
  5. Janusz Czelakowski
    Pages 99-154
  6. Janusz Czelakowski
    Pages 155-186
  7. Janusz Czelakowski
    Pages 207-227
  8. Janusz Czelakowski
    Pages 229-252
  9. Back Matter
    Pages 253-292

About this book


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 algebras.  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 its behavior 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.


abstract algebraic logic commutator commutator theory equational logic quasivarieties universal algebra

Authors and affiliations

  • Janusz Czelakowski
    • 1
  1. 1.Opole UniversityOpolePoland

Bibliographic information