Ockham Algebras [Hardcover]

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 Algebrasis the perfect introduction to the subject for graduate students and researchers studying algebra and lattice theory.

Introduction: Ordered Sets, Lattices, and Universal Algebra
1. Examples of Ockham Algebras, the Berman Classes
2. Congruence Relations
3. Subdirectly Irreducible Algebras
4. Duality Theory
5. The Lattice of Subvarieties
6. Fixed Points
7. Fixed Point Separating Congruences
8. Congruences on K1.1-Algebras
9. MS-Spaces; Fences, Crowns, ...
10. The Dual Space of a Finite Simple Ockham Algebra
11. Relative Ockham Algebras
12. Double MS-Algebras
13. Subdirectly Irreducible Double MS-Algebras
14. Congruences on Double MS-Algebras
15. Singles and Doubles
Bibliography
Notation Index
Index

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