The Equationally Defined Commutator
A Study in Equational Logic and Algebra
(Sprache: Englisch)
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...
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Klappentext zu „The Equationally Defined Commutator “
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.
Inhaltsverzeichnis zu „The Equationally Defined Commutator “
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.
Bibliographische Angaben
- Autor: Janusz Czelakowski
- 2015, 1st ed. 2015, IX, 292 Seiten, Maße: 16 x 24,1 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 3319211994
- ISBN-13: 9783319211992
Sprache:
Englisch
Pressezitat
"In this book, commutator theory is investigated from the perspective of algebraic logic. ... The book is addressed to algebraists and logicians interested in recent developements in the area of equational logic and the methods of abstract algebraic logic." (Ivan Chajda, zbMATH 1352.08001, 2017)Kommentar zu "The Equationally Defined Commutator"
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