Ockham Algebras by T. S. BlythOckham Algebras by T. S. Blyth

Ockham Algebras

byT. S. Blyth, J. C. Varlet

Hardcover | October 1, 1993

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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 seeminglymodest 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 towhich 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 involvingmany problems of a combinatorial nature. Written with the graduate student in mind, this book provides an ideal overview of this are of increasing interest.
T. S. Blyth is at University of St Andrews. J. C. Varlet is at University of Liege.
Title:Ockham AlgebrasFormat:HardcoverDimensions:250 pages, 9.21 × 6.14 × 0.79 inPublished:October 1, 1993Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198599382

ISBN - 13:9780198599388

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Table of Contents

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 K11-algebras9. MS-spaces; fences, crowns, ...10. The dual space of a finite simples Ockham algebra11. Relative Ockham algebras12. Double MS-algebras13. Subdirectly irreducible double MS-algebras14. Congruences on double MS-algebras15. Singles and doublesBibliographyNotation indexIndex

Editorial Reviews

`The book provides a self-contained and readable account of the theory of Ockham Algebras......this book will be a valuable reference text leading to the most recent results of research'Monatshefte fur Mathematik Vol 123 No 1