The Lattice of Subquasivarieties of a Locally Finite Quasivariety

1. Front Matter

   Pages I-XV

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2. Introduction and Background

   • Jennifer Hyndman, J. B. Nation

   Pages 1-10

3. Structure of Lattices of Subquasivarieties

   • Jennifer Hyndman, J. B. Nation

   Pages 11-36

4. Omission and Bases for Quasivarieties

   • Jennifer Hyndman, J. B. Nation

   Pages 37-47

5. Analyzing \(\mathop{\mathrm{L_{q}}}\nolimits (\mathcal{K})\)

   • Jennifer Hyndman, J. B. Nation

   Pages 49-64

6. Unary Algebras with 2-Element Range

   • Jennifer Hyndman, J. B. Nation

   Pages 65-102

7. 1-Unary Algebras

   • Jennifer Hyndman, J. B. Nation

   Pages 103-120

8. Pure Unary Relational Structures

   • Jennifer Hyndman, J. B. Nation

   Pages 121-132

9. Problems

   • Jennifer Hyndman, J. B. Nation

   Pages 133-134

10. Back Matter

    Pages 135-162

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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.

• Quasivariety
• Locally Finite
• Lattice
• Unary Algebra
• Relational Structure
• Subquasivariety
• Quasi-equation

• Department of Mathematics and Statistics, University of Northern British Columbia, Prince George, Canada

  Jennifer Hyndman

• Department of Mathematics, University of Hawaii, Honolulu, USA

  J. B. Nation

Jennifer Hyndman was a founding faculty member of the University of Northern British Columbia.  There she honed her passion for teaching that led to her winning the Canadian Mathematical Society Excellence in Teaching Award. When not engrossed in research on natural duality theory or quasi-equational theory she can be found in a dance studio learning jazz, modern, and ballet choreography.

J. B. Nation is professor emeritus at the University of Hawaii.  His research interests include lattice theory, universal algebra, coding theory and bio-informatics.  He enjoys running, refereeing soccer, and playing jazz flugelhorn.

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