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Tables of Contents for General Lattice Theory
Chapter/Section Title
Page #
Page Count
Preface and Acknowledgment
xi
Preface to the Second Edition
xv
Introduction
xvii
First Concepts
Two Definitions of Lattices
1
10
How to Describe Lattices
11
8
Some Algebraic Concepts
19
16
Polynomials, Identities, and Inequalities
35
7
Free Lattices
42
20
Special Elements
62
17
Further Topics and References
69
5
Problems
74
5
Distributive Lattices
Characterization and Representation Theorems
79
12
Polynomials and Freeness
91
7
Congruence Relations
98
18
Boolean Algebras
116
15
Topological Representation
131
16
Pseudocomplementation
147
22
Further Topics and References
159
7
Problems
166
3
Congruences and Ideals
Weak Projectivity and Congruences
169
12
Distributive, Standard, and Neutral Elements
181
12
Distributive, Standard, and Neutral Ideals
193
6
Structure Theorems
199
12
Further Topics and References
208
2
Problems
210
1
Modular and Semimodular Lattices
Modular Lattices
211
14
Semimodular Lattices
225
8
Geometric Lattices
233
17
Partition Lattices
250
13
Complemented Modular Lattices
263
32
Further Topics and References
285
7
Problems
292
3
Varieties of Lattices
Characterizations of Varieties
295
12
The Lattice of Varieties of Lattices
307
8
Finding Equational Bases
315
14
The Amalgamation Property
329
14
Further Topics and References
338
2
Problems
340
3
Free Products
Free Products of Lattices
343
20
The Structure of Free Lattices
363
9
Reduced Free Products
372
12
Hopfian Lattices
384
15
Further Topics and References
390
4
Problems
394
5
Concluding Remarks
399
4
Bibliography
403
60
Table of Notation
463
144
A Retrospective
Major Advances
466
8
Notes on Chapter I
474
5
Notes on Chapter II
479
4
Notes on Chapter III
483
1
Notes on Chapter IV
484
4
Notes on Chapter V
488
2
Notes on Chapter VI
490
4
Lattices and Universal Algebras
494
5
B Distributive Lattices and Duality by B. Davey, H. Priestley
Introduction
499
1
Basic Duality
500
5
Distributive Lattices with Additional Operations
505
3
Distributive Lattices with V-preserving Operators, and Beyond
508
1
The Natural Perspective
509
5
Congruence Properties
514
1
Freeness, Coproducts, and Injectivity
515
4
C Congruence Lattices by G. Gratzer, E. T. Schmidt
The Finite Case
519
8
The General Case
527
2
Complete Congruences
529
2
D Continuous Geometry by F. Wehrung
The von Neumann Coordinatization Theorem
531
2
Continuous Geometries and Related Topics
533
7
E Projective Lattice Geometries by M. Greferath, S. Schmidt
Background
540
3
A Unified Approach to Lattice Geometry
543
6
Residuated Maps
549
6
F Varieties of Lattices by P. Jipsen, H. Rose
The Lattice A
555
11
Generating Sets of Varieties
566
1
Equational Bases
567
2
Amalgamation and Absolute Retracts
569
3
Congruence Varieties
572
3
G Free Lattices by R. Freese
Whitman's Solutions; Basic Results
575
2
Classical Results
577
1
Covers in Free Lattices
578
4
Semisingular Elements and Tschantz's Theorem
582
2
Applications and Related Areas
584
8
H Formal Concept Analysis by B. Ganter and R. Wille
Formal Contexts and Concept Lattices
592
4
Applications
596
3
Sublattices and Quotient Lattices
599
1
Subdirect Products and Tensor Products
600
3
Lattice Properties
603
4
New Bibliography
607
34
Index
641