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.
Rezensionen / Stimmen
the first attempt to give a systematic and self-contained account of the research in this area. The text is well and clearly written, and it contains references to the literature. Many examples illustrate and sharpen the theory. This book could form a stimulating introduction for a student contemplating research in this area. * Zentrallblatt fure Mathematik, Band 835/96. * 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 *
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Für höhere Schule und Studium
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Gewebe-Einband
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Höhe: 229 mm
Breite: 152 mm
Dicke: 18 mm
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ISBN-13
978-0-19-859938-8 (9780198599388)
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Schweitzer Klassifikation
Autor*in
Professor, Mathematical InstituteProfessor, Mathematical Institute, University of St Andrews
Professor, Institute of MathematicsProfessor, Institute of Mathematics, University of Liege, Belgium
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
