# General Lattice Theory: Second edition

Springer Science & Business Media, 21.11.2002 - 663 Seiten
In 20 years, tremendous progress has been made in Lattice Theory. Nevertheless, the change is in the superstructure not in the foundation. Accordingly, I decided to leave the book unchanged and add appendices to record the change. In the first appendix: Retrospective, I briefly review developments from the point of view of this book, specifically, the major results of the last 20 years and solutions of the problems proposed in this book. It is remarkable how many difficult problems have been solved! I was lucky in getting an exceptional group of people to write the other appendices: Brian A. Davey and Hilary A. Priestley on distributive lattices and duality, Friedrich Wehrung on continuous geometries, Marcus Greferath and Stefan E. Schmidt on projective lattice geometries, Peter Jipsen and Henry Rose on varieties, Ralph Freese on free lattices, Bernhard Ganter and Rudolf Wille on formal concept analysis; Thomas Schmidt collaborated with me on congruence lattices. Many of these same people are responsible for the definitive books on the same subjects. I changed very little in the book proper. The diagrams have been redrawn and the book was typeset in ~1EX. To bring the notation up-to-date, I substituted ConL for C(L), IdL for I(L), and so on. Almost 200 mathematicians helped me with this project, from correcting typos to writing long essays on the topics that should go into Retrospective. The last section of Retrospective lists the major contributors. My deeply felt thanks to all of them.

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### Inhalt

 Chapter I First Concepts 1 Chapter II Distributive Lattices 79 Chapter III Congruences and Ideals 169 Chapter IV Modular and Semimodular Lattices 211 Chapter V Varieties of Lattices 295 Chapter VI Free Products 343 Concluding Remarks 399 Bibliography 403
 Appendix B Distributive Lattices and Duality 499 Appendix C Congruence Lattices 519 Appendix D Continuous Geometry 531 Appendix E Projective Lattice Geometries 539 Appendix F Varieties of Lattices 555 Appendix G Free Lattices 575 Appendix H Applied Lattice Theory Formal Concept Analysis 591 New Bibliography 607

 Table of Notation 463 Appendix A Retrospective 465
 Index 641 Urheberrecht

### Beliebte Passagen

Seite 636 - ET SCHMIDT, The ideal lattice of a distributive lattice with 0 is the congruence lattice of a lattice, Acta Sci.
Seite 626 - On the word problem for the modular lattice with four free generators. Math. Ann.
Seite 630 - KM Koh and TC Chua. A characterization of the lattice of convex sublattices of a finite lattice. Tamkang J. Math. 10 ) 1979).
Seite 406 - Primitive satisfaction and equational problems for lattices and other algebras, Trans.

### Verweise auf dieses Buch

 Mathematical Principles of Fuzzy LogicEingeschränkte Leseprobe - 1999
 Quadratic Algebras, Clifford Algebras, and Arithmetic Witt GroupsKeine Leseprobe verfügbar
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