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

• Main Author: Czelakowski, Janusz (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2015.
• Edition: 1st ed. 2015.
• Subjects: Mathematics.; Associative rings.; Rings (Algebra).; Commutative algebra.; Commutative rings.; Group theory.; Group Theory and Generalizations.; Commutative Rings and Algebras.; Associative Rings and Algebras.

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 a...

Table of Contents:

• 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.