foreword

preface

chapter 1 universal algebra and lattice-ordered algebras

1.1 universal algebra

1.2 lattice-ordered algebras

1.3 priestley duality of lattice-ordered algebras

chapter 2 ockham algebras

2.1 subclasses

2.2 the subdirectly irreducible algebras

2.3 ockham chains

2.4 the structures of finite simple ockham algebras

2.5 isotone mappings on ockham algebras

chapter 3 extended ockham algebras

3.1 definition and basic congruences

3.2 the subdirectly irreducible algebras

3.3 symmetric extended de morgan algebras

chapter 4 double ockham algebras

4.1 notions and basic results

4.2 commuting double ockham algebras

.4.3 balanced double ockham algebras

chapter 5 pseudocomplemented and demi-pseudocomplemerited algebras

5.1 pseudocomplemented algebras

5.2 the subdirectly irreducible p-algebras

5.3 double pseudocomplemented algebras

5.4 ideals and filters

5.5 demi-pseudocomplemented algebras

chapter 6 ockham algebras with pseudocomplementation 6.1 notions and basic results

6.2 the structure of congruence lattices

6.3 the subdirectly irreducible algebras

6.4 the subvarieties of variety pk1,1

6.5 ideals and filters in po-algebras

chapter 7 oekham algebras with double pseudocomplementation

7.1 notions and properties

7.2 the structure of the subdirectly irreducible algebras

chapter 8 ockham algebras with balanced pseudocomplementation

8.1 introduction

8.2 the structures of the congruence lattices

8.3 priestley duality and subdirectly irreducible algebras

8.4 equational bases

8.5 the subvarieties of bpo determined by axioms

chapter 9 ockham algebras with demi-pseudocomplementation

9.1 notions and basic results

9.2 k1,1-algebras with demi-pseudocomplementation

9.3 weak stone-ockham algebras

chapter 10 ockham algebras with balanced demipseudocomplementation

10.1 basic results

10.2 the subdirectly irreducible algebras

chapter 11 coherent congruences on some lattice-ordered algebras

ll.1 introduction

11.2 on double ms-algebras

11.3 on symmetric extended de morgan algebras

chapter 12 the endomorphism kernel property in ockham algebras

12.1 the endomorphism kernel property

12.2 ockham algebras

12.3 de morgan algebras

bibliography

notation index

index

With the development of information science and theoretical computer science, lattice-ordered algebraic structure theory has played a more and more important role in theoretical and applied science. Not only is it an important branch of modern mathematics, but it also has broad and important applications in algebra, topology, fuzzy mathematics and other applied sciences such as coding theory, computer programs, multi-valued logic and science of information systems, etc. The research in distributive lattices with unary operations has made great progress in the past three decades, since Joel Berman first introduced the distributive lattices with an additional unary operation in 1978, which were named Ockham algebras by Goldberg a year later. This is due to those researchers who are working on this subject, such as Adams, Beazer, Berman, Blyth, Davey, Goldberg, Priestley, Sankappanavar and Varlet.