Introduction to Lattices and Order

by B. A. Davey, H. A. Priestley

Overview

Ordered structures have been increasingly recognized in recent years due to an explosion of interest in theoretical computer science and all areas of discrete mathematics. This book covers areas such as ordered sets and lattices. A key feature of ordered sets, one which is emphasized in the text, is that they can be represented pictorially. Lattices are also considered as algebraic structures and hence a purely algebraic study is used to reinforce the ideas of homomorphisms and of ideals encountered in group theory and ring theory. Exposure to elementary abstract algebra and the rotation of set theory are the only prerequisites for this text. For the new edition, much has been rewritten or expanded and new exercises have been added.

Product Details

ISBN-13:	9780521784511
Publisher:	Cambridge University Press
Publication date:	04/18/2002
Edition description:	Revised Edition
Pages:	312
Product dimensions:	5.98(w) x 9.02(h) x 0.67(d)

Table of Contents

Preface; Preface to the first edition; 1. Ordered sets; 2. Lattices and complete lattices; 3. Formal concept analysis; 4. Modular, distributive and Boolean lattices; 5. Representation theory: the finite case; 6. Congruences; 7. Complete lattices and Galois connections; 8. CPOs and fixpoint theorems; 9. Domains and information systems; 10. Maximality principles; 11. Representation: the general case; Appendix A. A topological toolkit; Appendix B. Further reading; Notation index; Index.

Editorial Reviews

"...this second edition merits the same five stars as the first."
Mathematical Reviews


"The book is written in a very engaging and fluid style. The understanding of the content is aided tremendously by the very large number of beautiful lattice diagrams...The book provides a wonderful and accessible introduction to lattice theory, of equal interest to both computer scientists and mathematicians."
Jonathan Cohen, SIGACT News

From the Publisher

This second edition of a text devoted to ordered sets and lattices and their contemporary applications presents a reorganization and updating of the content of the first (1990) edition. There is a fresh treatment of fixpoint theorems and more emphasis on Galois connections. New exercises have also been added to this edition. Written for advanced undergraduate and first-year graduate students, the book requires background in abstract algebra and the notation of set theory. Davey is affiliated with La Trobe University. Priestley is affiliated with the University of Oxford. Annotation c. Book News, Inc., Portland, OR (booknews.com)