The equationally-defined commutator : a study in equational logic and algebra /: a study in equational logic and algebra. (2015)

• Record Type: Book
• Further Information: Note: Janusz Czelakowski.
• Authors: Czelakowski, Janusz
• Contents: Synopsis; Contents; 1 Introduction; 2 Basic Properties of Quasivarieties; 2.1 Quasi-Identities; 2.2 Rules of Inference; 2.3 Equational Logics; 2.4 Relative Congruences; 2.5 Free Algebras; 2.6 More on Congruences; 2.7 Properties of Equational Theories; 2.8 Epimorphisms and Isomorphic Embeddings of the Lattice of Theories; 2.9 The Kernels of Epimorphisms; 3 Commutator Equations and the Equationally-DefinedCommutator; 3.1 Commutator Equations and the Equationally-Defined Commutator of Congruences; 3.1.1 The Standard Commutator; 3.2 The Equationally-Defined Commutator of Equational Theories 3.3 More on Epimorphisms and the Equationally-DefinedCommutator3.4 The Relative Shifting Property and the Commutator; 3.5 Day Implication Systems and the Relative Shifting Property; 3.6 The Relative Cube Property; 3.6.1 The Relative Shifting Property and the Relative Cube Property are Equivalent Properties; 4 Centralization Relations; 4.1 Four Centralization Relations for Quasivarieties; 4.2 Centralization Relations in the Sense of One-Term Conditions; 4.2.1 Three More Centralization Relations; 4.3 Generating Sets of Commutator Equations; 5 Additivity of the Equationally-Defined Commutator 5.1 Conditions (C1) and (C2)5.2 Additivity of the Equationally-Defined Commutator of Equational Theories; 5.2.1 The Equationally-Defined Commutator on the Free Algebra FQ(ω); 5.3 Restricted Distributivity and Additivity of the Equationally-Defined Commutator; 5.4 Semilattices and Restricted Distributivity; 5.5 A Characterization of the Equationally-Defined Commutator; 6 Modularity and Related Topics; 6.1 Relative Congruence-Modularity and the Equationally-Defined Commutator; 6.2 The Extension Principle; 6.3 Distributivity in the Lattice of Equational Theories of RCM Quasivarieties 6.4 Generating Sets of Commutator Equations in Varieties6.4.1 Gumm Terms; 6.4.2 Varieties with Congruence-Permutable Congruences; 6.4.3 Groups; 6.4.4 Equivalence Algebras; 6.5 Various Commutators in Varieties; 7 Additivity of the Equationally-Defined Commutator and Relatively Congruence-Distributive Subquasivarieties; 7.1 Relatively Finitely Subdirectly Irreducible Algebras; 7.2 Prime Algebras; 7.3 Semiprime Algebras; 8 More on Finitely Generated Quasivarieties; 8.1 Generating Sets for the Equationally-Defined Commutator in Finitely Generated Quasivarieties 8.2 Triangular Irreducibility of Congruences8.3 Equationally-Definable m-Triangular Meets of Relatively Principal Congruences (m-EDTPM); 8.4 Properties Related to m-EDTPM; 9 Commutator Laws in Finitely Generated Quasivarieties; 9.1 Iterations of Generating Sets; 9.2 Pure Commutator Terms and Their Interpretations; 9.3 Nilpotency; 9.4 Identities Weaker than Nilpotency; 9.5 Commutator Identities in Finitely Generated Quasivarieties; A Algebraic Lattices; A.1 Partially Ordered Sets; A.2 Semilattices and Lattices; A.3 Extensions by Ideals. Algebraic Lattices
• Publisher Details: Cham : Birkhäuser
• Publication Date: 2015
• Extent: 1 online resource
• Subjects: 511.324; Algebraic logic; Equations; MATHEMATICS / General; Algebraic logic; Equations; Electronic books; Electronic books
• Languages: English
• ISBNs: 9783319212005; 3319212001
• Related ISBNs: 9783319211992; 3319211994
• Notes: Note: Includes bibliographical references and indexes.; Note: Online resource; title from PDF title page (EBSCO, viewed September 12, 2015)
• Access Rights: Legal Deposit; Only available on premises controlled by the deposit library and to one user at any one time; The Legal Deposit Libraries (Non-Print Works) Regulations (UK).
• Access Usage: Restricted: Printing from this resource is governed by The Legal Deposit Libraries (Non-Print Works) Regulations (UK) and UK copyright law currently in force.