Combines the techniques of an introductory text with those of a monograph to introduce the general reader to lattice theory & to bring the expert up to date on the most recent developments. This present edition has been significantly updated & expanded.
Author(s): George A Gratzer
Series: Pure and applied mathematics : a series of monographs and textbooks
Publisher: AP
Year: 1978
Language: English
Pages: 397
General Lattice Theory......Page 4
Copyright Page......Page 5
Contents......Page 8
Preface and Acknowledgements......Page 10
Introduction......Page 12
1. Two Definitions of Lattices......Page 16
2. How to Describe Lattices......Page 24
3. Some Algebraic Concepts......Page 30
4. Polynomials, Identities, and Inequalities......Page 41
5. Free Lattices......Page 47
6. Special Elements......Page 62
Further Topics and References......Page 67
Problems......Page 71
1. Characterization Theorems and Representation Theorems......Page 74
2. Distributive, Standard, and Neutral Elements......Page 153
3. Congruence Relations......Page 88
4. Boolean Algebras R-generated by Distributive Lattices......Page 101
5. Topological Representation......Page 114
6. Distributive Lattices with Pseudocomplementation......Page 126
Further Topics and References......Page 135
Problems......Page 141
1. Weak Projectivity and Congruences......Page 144
3. Distributive, Standard, and Neutral Ideals......Page 161
4. Structure Theorems......Page 166
Further Topics and References......Page 173
Problems......Page 174
1. Modular Lattices......Page 176
2. Semimodular Lattices......Page 187
3. Geometric Lattices......Page 193
4. Partition Lattices......Page 207
5. Complemented Modular Lattices......Page 216
Further Topics and References......Page 233
Problems......Page 239
1. Characterizations of Equational Classes......Page 242
2. The Lattice of Equational Classes of Lattices......Page 251
3. Finding Equational Bases......Page 258
4. The Amalgamation Property......Page 267
Further Topics and References......Page 275
Problems......Page 277
1. Free Products of Lattices......Page 280
2. The Structure of Free Lattices......Page 297
3. Reduced Free Products......Page 303
4. Hopfien Lattices......Page 313
Further Topics and References......Page 318
Problems......Page 321
CONCLUDING REMARKS......Page 326
BIBLIOGRAPHY......Page 331
TABLE OF NOTATION......Page 377
INDEX......Page 380
