國立虎尾科技大學 |

The equationally-defined commutator = a study in equational logic and algebra /

Record Type:	Language materials, printed : Monograph/item
Title/Author:	The equationally-defined commutator/ by Janusz Czelakowski.
Reminder of title:	a study in equational logic and algebra /
Author:	Czelakowski, Janusz.
Published:	Cham :Imprint: Birkhauser, : 2015.,
Description:	ix, 292 p. :ill., digital ; : 24 cm.;
Contained By:	Springer eBooks
Subject:	Associative Rings and Algebras. -
Online resource:	http://dx.doi.org/10.1007/978-3-319-21200-5
ISBN:	9783319212005

The equationally-defined commutator = a study in equational logic and algebra /
Czelakowski, Janusz.

The equationally-defined commutatora study in equational logic and algebra /[electronic resource] :by Janusz Czelakowski. - Cham :Imprint: Birkhauser,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

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

672306
Associative Rings and Algebras.

LC Class. No.: QA10

Dewey Class. No.: 511.324

The equationally-defined commutator = a study in equational logic and algebra /
LDR:02564nam a2200313 a 4500 001 838606
003 DE-He213
005 20160413155223.0
006 m d
007 cr nn 008maaau
008 160616s2015 gw s 0 eng d
020 $a 9783319212005 $q (electronic bk.)
020 $a 9783319211992 $q (paper)
024 7 $a 10.1007/978-3-319-21200-5 $2 doi
035 $a 978-3-319-21200-5
040 $a GP $c GP
041 0 $a eng
050 4 $a QA10
072 7 $a PBG $2 bicssc
072 7 $a MAT002010 $2 bisacsh
082 0 4 $a 511.324 $2 23
090 $a QA10 $b .C998 2015
100 1 $a Czelakowski, Janusz. $3 1069846
245 1 4 $a The equationally-defined commutator $h [electronic resource] : $b a study in equational logic and algebra / $c by Janusz Czelakowski.
260 $a Cham : $c 2015. $b Imprint: Birkhauser, $b Springer International Publishing :
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 2 4 $a Associative Rings and Algebras. $3 672306
650 2 4 $a Commutative Rings and Algebras. $3 672054
650 2 4 $a Group Theory and Generalizations. $3 672112
650 1 4 $a Mathematics. $3 527692
650 0 $a Equations. $3 579868
650 0 $a Algebraic logic. $3 633629
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer eBooks
856 4 0 $u http://dx.doi.org/10.1007/978-3-319-21200-5
950 $a Mathematics and Statistics (Springer-11649)