Ockham algebras
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Bibliographic Information
Ockham algebras
Oxford University Press, 1994
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"Oxford science publications"
Includes bibliographical references
Description and Table of Contents
Description
An Ockham algebra is a natural generalization of a well known and important notion of a boolean algebra. Regarding the latter as a bounded distributive lattice with complementation (a dual automorphism of period 2) by a dual endomorphism that satisfies the de Morgan laws, this seemingly modest generalization turns out to be extemely wide. The variety of Ockham algebras has infinitely many subvarieties including those of de Morgan algebras, Stone algebras, and
Kleene algebras. Folowing pioneering work by Berman in 1977, many papers have appeared in this area oflattice theory to which several important results in the theory of universal algebra are highly applicable. This is the first unified account of some of this research. Particular emphasis is placed on
Priestly's topological duality, which invloves working with ordered sets and order-reversing maps, hereby involving many problems of a combinatorial nature. Written with the graduate student in mind, this book provides an ideal overview of this are of increasing interest.
Table of Contents
- 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 simples 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
by "Nielsen BookData"
