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Summary:

This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.

Table of Contents:

• Intro; Preface; Contents; List of Figures; List of Tables; Chapter 1. Introduction and Background; 1.1. Introduction; 1.2. Background; 1.3. Review of Complete Lattices; Chapter 2. Structure of Lattices of Subquasivarieties; 2.1. Completely Join Irreducible Quasivarieties; 2.2. Reflections; 2.3. Completely Meet Irreducible Quasivarieties; 2.4. Quasivarieties of Modular Lattices; 2.5. Quasivarieties of Abelian Groups; 2.6. Quasivarieties of Infinite Type; Chapter 3. Omission and Bases for Quasivarieties; 3.1. Characterizing Quasivarieties by Excluded Subalgebras; 3.2. Pseudoquasivarieties.
• Chapter 4. Analyzing Lq(K)4.1. Algorithms; 4.2. Fermentability; 4.3. Equational Quasivarieties; 4.4. The Atoms of Lq(K); 4.5. The Variety Z; 4.6. Synopsis; Chapter 5. Unary Algebras with 2-Element Range; 5.1. The Variety Generated by M; 5.2. Illustrating the Algorithms: 1-Generated Algebras; 5.3. Illustrating the Algorithms: 2-Generated Algebras; 5.4. Uncountably Many Subquasivarieties; 5.5. Q-Universality of M; Chapter 6. 1-Unary Algebras; 6.1. 1-Unary Algebras With and Without 0; 6.2. Some Quasivarieties Nr, s0; 6.3. Some Quasivarieties Nr, s; Chapter 7. Pure Unary Relational Structures.
• 7.1. Pure Unary Relational Quasivarieties7.2. Quasicritical Lemmas; 7.3. One Unary Relation; 7.4. Two Unary Relations; 7.5. Adding a Constant; Chapter 8. Problems; Appendix A. Properties of Lattices of Subquasivarieties; A.1. Representations of Quasivariety Lattices; A.2. Representations of Quasivariety Lattices; A.3. Basic Consequences of the Representations; A.4. Equaclosure Operators; A.5. Examples of Quasivariety Lattices; A.6. The Quasivariety Generated by a Quasiprimal Algebra; A.7. Miscellaneous; Bibliography; Symbol Index; Author Index; Subject Index.

Author/Creator:

Hyndman, Jennifer , author

Contributors:

Nation, J. B. (James Bryant), 1948- , author

Languages:

English

Language Notes:

Item content: English

Main Work:

The lattice of subquasivarieties of a locally finite quasivariety [by Hyndman, J.]

Other Related Resources:

Print version: Lattice of subquasivarieties of a locally finite quasivariety [by Hyndman, J.] (Cham : Springer, 2018 — ISBN 3319782347; ISBN 9783319782348; OCLC Number 1024258340)

Related Series:

CMS books in mathematics

Subjects:

Quasivarieties (Universal algebra)

General Notes:

Includes bibliographical references and index.
Description based on: Online resource; title from PDF title page (EBSCO, viewed August 31, 2018).

Physical Description:

1 online resource.

Digital Characteristics:

text file

Call Numbers:

QA251 .H963 2018eb

ISBNs:

9783319782355 (electronic bk.)
3319782355 (electronic bk.)
9783319782362 (print) [Invalid]
3319782363
9783319782348 [Invalid]
3319782347 [Invalid]

Other Standard Numbers:

Digital Object Identifier: 10.1007/978-3-319-78235-5
[Unknown Type]: 10.1007/978-3-319-78

OCLC Numbers:

1050321311