Ockham Algebras

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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.

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Product Details

  • ISBN-13: 9780198599388
  • Publisher: Oxford University Press, USA
  • Publication date: 10/28/1994
  • Series: Oxford Science Publications Series
  • Pages: 256
  • Product dimensions: 6.38 (w) x 9.50 (h) x 0.78 (d)

Meet the Author

University of St Andrews

University of Liege

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Table of Contents

0 Ordered sets, lattices, and universal algebra 1
1 Examples of Ockham algebras; the Berman classes 8
2 Congruence relations 20
3 Subdirectly irreducible algebras 37
4 Duality theory 52
5 The lattice of subvarieties 75
6 Fixed points 105
7 Fixed point separating congruences 115
8 Congruences on K[subscript 1,1]-algebras 133
9 MS-spaces; fences, crowns, ... 149
10 The dual space of a finite simple Ockham algebra 164
11 Relative Ockham algebras 179
12 Double MS-algebras 187
13 Subdirectly irreducible double MS-algebras 197
14 Congruences on double MS-algebras 207
15 Singles and doubles 216
Bibliography 231
Notation index 237
Index 239
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