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

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

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...

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Bibliographic Details
Published in:Springer eBooks
Main Author: Czelakowski, Janusz (Author)
Corporate Author: SpringerLink (Online service)
Format: 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.
Mathematics.
Group Theory and Generalizations.
Commutative Rings and Algebras.
Associative Rings and Algebras.
Online Access:http://dx.doi.org/10.1007/978-3-319-21200-5
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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.

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