General Lattice Theory: Second editionSpringer 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. |
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 |
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 |
607 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
a₁ algebraic lattice Arguesian atoms B. A. Davey b₁ Boolean algebras Boolean lattice bounded lattice characterization compact complemented lattice complemented modular lattice complete lattice concept congruence lattice congruence relation Corollary countable define Definition denote direct product dual ideal duality dually E. T. Schmidt embedded equivalent Exercise exists Figure finite distributive lattice finite lattice free lattice free product geometric lattice Grätzer and E. T. hence holds homomorphism identity implies infinite isomorphic join-semilattice Jónsson Lakser lattice and let lattice theory Lemma Math maximal chain modular lattice nonempty one-to-one partial lattice partial ordering polynomials poset prime ideal Problem projective geometry proof of Theorem Prove pseudocomplemented quotient R. N. McKenzie R. P. Dilworth relatively complemented representation result Section semilattice semimodular lattice Show Stone algebras subalgebra subdirectly irreducible subdirectly irreducible lattice sublattice subset subspace topological variety of lattices verify
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.
Verweise auf dieses Buch
Mathematical Principles of Fuzzy Logic Vilém Novák,Irina Perfilieva,J. Mockor Eingeschränkte Leseprobe - 1999 |
Quadratic Algebras, Clifford Algebras, and Arithmetic Witt Groups Alexander Polishchuk,Leonid Positselski Keine Leseprobe verfügbar |