Lattice Theory: Foundation

Authors: Grätzer, George

  • Authoritative introduction to lattice theory for graduate students
  • Standard reference work for researchers in this area
  • First of two volumes of the substantially revised and enlarged third edition
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About this Textbook

This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Over 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics.

“Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Garrett Birkhoff (Bulletin of the American Mathematical Society)

“Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” (Mathematical Reviews)

About the authors

George Grätzer, Member of the Canadian Academy of Sciences and Foreign Member of the Hungarian Academy of Sciences, is the author of 26 books in five languages and about 260 articles, most of them on his research in lattice theory.

Reviews

From the reviews:

“Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Garrett Birkhoff (Bulletin of the American Mathematical Society

“Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” (Mathematical Reviews)

“This book has a long history maturing in contents and details over a period of more than 40 years. … For many years to come it will be the standard textbook and main reference for everybody interested in Lattice Theory. … It contains more than 1,000 exercises, a bibliography of 742 items, and a useful glossary of notation. All this, together with the very clear style of presentation, makes the book an extremely valuable contribution to the theory of lattices.” (M. Mitsch, Monatshefte für Mathematik, Vol. 164 (4), 2011)

“This book is a new version of the author’s famous book on lattice theory, which appeared in several editions … . The bibliography was updated and now contains 742 items. … the integration of the former appendices into the main body of the book was a very good idea, as it will help the reader to get a clearer picture of the current state of the art in lattice theory.” (G. Eigenthaler, Zentralblatt MATH, Vol. 1233, 2012)


Table of contents (7 chapters)

Buy this book

eBook $64.99
price for USA (gross)
  • ISBN 978-3-0348-0018-1
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Softcover $84.95
price for USA
  • ISBN 978-3-0348-0017-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Rent the eBook  
  • Rental duration: 1 or 6 month
  • low-cost access
  • online reader with highlighting and note-making option
  • can be used across all devices
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Bibliographic Information

Bibliographic Information
Book Title
Lattice Theory: Foundation
Authors
Copyright
2011
Publisher
Birkhäuser Basel
Copyright Holder
Springer Basel AG
eBook ISBN
978-3-0348-0018-1
DOI
10.1007/978-3-0348-0018-1
Softcover ISBN
978-3-0348-0017-4
Edition Number
1
Number of Pages
XXX, 614
Topics