Ockham Algebras

by T. S. Blyth, J. C. Varlet

Overview

Ockham algebras—the natural generalization of a well known and important notion of a boolean algebra—has an infinite amount of subvarieties, including those of de Morgan, Stone, and Kleene algebras. This book, the first unified account of the subject, details the many important breakthroughs that have occurred in this area of lattice theory since Berman's pioneering work in 1977. Particular emphasis is placed on Priestley's topological duality, which involves ordered sets and order-reversing maps. With its many illustrative examples and substantial bibliography, Ockham Algebras is the perfect introduction to the subject for graduate students and researchers studying algebra and lattice theory.

Product Details

ISBN-13:	9780198599388
Publisher:	Oxford University Press
Publication date:	11/10/1994
Series:	Oxford Science Publications Series
Pages:	250
Product dimensions:	9.00(w) x 6.00(h) x 0.69(d)

About the Author

University of St Andrews

University of Liege

Table of Contents

Introduction: Ordered Sets, Lattices, and Universal Algebra1. Examples of Ockham Algebras, the Berman Classes2. Congruence Relations3. Subdirectly Irreducible Algebras4. Duality Theory5. The Lattice of Subvarieties6. Fixed Points7. Fixed Point Separating Congruences8. Congruences on K1.1-Algebras9 MS-Spaces; Fences, Crowns, ...10. The Dual Space of a Finite Simple Ockham Algebra11. Relative Ockham Algebras12. Double MS-Algebras13. Subdirectly Irreducible Double MS-Algebras14. Congruences on Double MS-Algebras15. Singles and DoublesBibliographyNotation IndexIndex

Editorial Reviews

"An Ockham algebra is a bounded distributive lattice enriched with a dual endomorphism. Particular classes of Ockham algebras are the well-known classes of Boolean algebras, De Morgan algebras and Stone algebras. It is thus not only a useful reference work for researchers but also a good introduction for beginning graduate students."—Mathematical Reviews

From the Publisher