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Catalogue Information
Field name	Details
Dewey Class	512.2
Title	The Equationally-Defined Commutator ([EBook]) : A Study in Equational Logic and Algebra / / by Janusz Czelakowski.
Author	Czelakowski, Janusz
Other name(s)	SpringerLink (Online service)
Edition statement	1st ed. 2015.
Publication	Cham : : Springer International Publishing : : Imprint: Birkhäuser, , 2015.
Physical Details	IX, 292 p. 3 illus. : online resource.
ISBN	9783319212005
Summary Note	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.:
Contents note	Introduction -- Basic Properties of Quasivarieties -- Commutator Equations and the Equationally Defined Commutator -- Centralization Relations -- Additivity of the Equationally Defined Commutator -- Modularity and Related Topics -- Additivity of the Equationally Defined Commutator and Relatively Congruence-Distributive Dub quasivarieties -- More on Finitely Generated Quasivarieties -- Commutator Laws in Finitely Generated Quasivarieties -- Appendix 1: Algebraic Lattices.- Appendix 2: A Proof of Theorem 3.3.4 for Relatively Congruence-Modular Quasivarieties -- Appendix 3: Inferential Bases for Relatively Congruence-Modular Quasivarieties.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site	http://dx.doi.org/10.1007/978-3-319-21200-5
Links to Related Works	Subject References: Associative rings . Associative Rings and Algebras . Commutative algebra . Commutative rings . Commutative Rings and Algebras . Group theory . Group Theory and Generalizations . Mathematics . Rings (Algebra) . Authors: Czelakowski, Janusz . Corporate Authors: SpringerLink (Online service) . Classification: 512.2 .

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The Equationally-Defined Commutator: A Study in Equational Logic and Algebra /

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