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Chapter 1 Universal Algebra and Lattice-ordered Algebras 1

1.1 Universal algebra 1

1.2 Lattice-ordered algebras 9

1.3 Priestley duality of lattice-ordered algebras 10

Chapter 2 Ockham Algebras 15

2.1 Subclasses 15

2.2 The subdirectly irreducible algebras 18

2.3 Ockham chains 26

2.4 The structures of finite simple Ockham algebras 28

2.5 Isotone mappings on Ockham algebras 34

Chapter 3 Extended Ockham Algebras 39

3.1 Definition and basic congruences 39

3.2 The subdirectly irreducible algebras 43

3.3 Symmetric extended de Morgan algebras 57

Chapter 4 Double Ockham Algebras 61

4.1 Notions and basic results 61

4.2 Commuting double Ockham algebras 63

4.3 Balanced double Ockham algebras 69

Chapter 5 Pseudocomplemented and Demi-pseudocomple-mented Algebras 79

5.1 Pseudocomplemented algebras 79

5.2 The subdirectly irreducible p-algebras 84

5.3 Double pseudocomplemented algebras 88

5.4 Ideals and filters 90

5.5 Demi-pseudocomplemented algebras 94

Chapter 6 Ockham Algebras with Pseudocomplementation 102

6.1 Notions and basic results 102

6.2 The structure of congruence lattices 105

6.3 The subdirectly irreducible algebras 113

6.4 The subvarieties of variety pK1,1 121

6.5 Ideals and filters in pO-algebras 126

Chapter 7 Ockham Algebras with Double Pseudocomple-mentation 133

7.1 Notions and properties 133

7.2 The structure of the subdirectly irreducible algebras 136

Chapter 8 Ockham Algebras with Balanced Pseudocomple-mentation 148

8.1 Introduction 148

8.2 The structures of the congruence lattices 150

8.3 Priestley duality and subdirectly irreducible algebras 157

8.4 Equationalbases 162

8.5 The subvarieties of bpO determined by axioms 168

Chapter 9 Ockham Algebras with Demi-pseudocomple-mentation 176

9.1 Notions and basic results 176

9.2 K1,1-algebras with demi-pseudocomplementation 180

9.3 Weak Stone-Ockham algebras 189

Chapter 10 Ockham Algebras with Balanced Demi-pseudocomplementation 195

10.1 Basic results 195

10.2 The subdirectly irreducible algebras 198

Chapter 11 Coherent Congruences on Some Lattice-ordered Algebras 211

11.1 Introduction 211

11.2 On double MS-algebras 211

11.3 On symmetric extended de Morgan algebras 219

Chapter 12 The Endomorphism Kernel Property in Ockham Algebras 229

12.1 The endomorphism kernel property 229

12.2 Ockham algebras 235

12.3 De Morgan algebras 238

Bibliography 247

Notation Index 253

Index 255