Overview
- New edition covers over 10 years of new results in the field
- Self-contained exposition presents the major results on congruence lattices of finite lattices
- Author is a well-known pioneering researcher in the field
- Features the author's signature "Proof-by-Picture" method and its conversion to transparencies
- Excellent graduate textbook and reference
- Includes supplementary material: sn.pub/extras
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Table of contents (25 chapters)
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Front Matter
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A Brief Introduction to Lattices
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Front Matter
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Some Special Techniques
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Front Matter
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Congruence Lattices of Finite Lattices
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Front Matter
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Congruence Lattices and Lattice Extensions
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Front Matter
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Keywords
About this book
This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method.
Key features:
* Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions
* Contains complete proofs, an extensive bibliography and index, and over 140 illustrations
* This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 yearsThe book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices.
Reviews of the first edition:
"There exist a lot of interesting results in this area of lattice theory, and some of them are presented inthis book. [This] monograph…is an exceptional work in lattice theory, like all the contributions by this author. … The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. Moreover, the author provides a series of companion lectures which help the reader to approach the Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007)
"The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations offinite lattices, with emphasis on the more 'geometric' aspects." —Mathematical Reviews
Authors and Affiliations
About the author
Bibliographic Information
Book Title: The Congruences of a Finite Lattice
Book Subtitle: A "Proof-by-Picture" Approach
Authors: George Grätzer
DOI: https://doi.org/10.1007/978-3-319-38798-7
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: Springer International Publishing Switzerland 2016
Softcover ISBN: 978-3-319-81748-4Published: 30 May 2018
eBook ISBN: 978-3-319-38798-7Published: 29 June 2016
Edition Number: 2
Number of Pages: XXXIV, 346
Number of Illustrations: 159 b/w illustrations
Topics: Order, Lattices, Ordered Algebraic Structures, Mathematical Logic and Foundations, Probability Theory and Stochastic Processes, Number Theory