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The equationally-defined commutatora...

Czelakowski, Janusz.

The equationally-defined commutatora study in equational logic and algebra /

Record Type:	Electronic resources : Monograph/item
Title/Author:	The equationally-defined commutatorby Janusz Czelakowski.
Reminder of title:	a study in equational logic and algebra /
Author:	Czelakowski, Janusz.
Published:	Cham :Springer International Publishing :2015.
Description:	ix, 292 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Algebraic logic.
Online resource:	http://dx.doi.org/10.1007/978-3-319-21200-5
ISBN:	9783319212005$q(electronic bk.)

The equationally-defined commutatora study in equational logic and algebra /
Czelakowski, Janusz.

The equationally-defined commutatora study in equational logic and algebra /[electronic resource] :by Janusz Czelakowski. - Cham :Springer International Publishing :2015. - ix, 292 p. :ill., digital ;24 cm.

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.

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.

ISBN: 9783319212005$q(electronic bk.)

Standard No.: 10.1007/978-3-319-21200-5doiSubjects--Topical Terms:

522723
Algebraic logic.

LC Class. No.: QA10

Dewey Class. No.: 511.324

The equationally-defined commutatora study in equational logic and algebra /
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245 1 4 $a The equationally-defined commutator $h [electronic resource] : $b a study in equational logic and algebra / $c by Janusz Czelakowski.
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300 $a ix, 292 p. : $b ill., digital ; $c 24 cm.
505 0 $a 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.
520 $a 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.
650 0 $a Algebraic logic. $3 522723
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650 1 4 $a Mathematics. $3 184409
650 2 4 $a Group Theory and Generalizations. $3 274819
650 2 4 $a Commutative Rings and Algebras. $3 274057
650 2 4 $a Associative Rings and Algebras. $3 274818
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