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The Congruences of a Finite Lattice

A "Proof-by-Picture" Approach

Authors: Grätzer, George

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  • 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
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eBook $69.99
price for Mexico (gross)
  • ISBN 978-3-319-38798-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for Mexico
  • ISBN 978-3-319-38796-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for Mexico
  • ISBN 978-3-319-81748-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this Textbook

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 years

The 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 in this 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 of finite lattices, with emphasis on the more 'geometric' aspects."   —Mathematical Reviews

About the authors

George A. Grätzer is a Hungarian-Canadian mathematician, specializing in lattice theory and universal algebra. He is also known for his books on LaTeX and his proof with E. Tamás Schmidt of the Grätzer-Schmidt theorem.

Table of contents (25 chapters)

Table of contents (25 chapters)

Buy this book

eBook $69.99
price for Mexico (gross)
  • ISBN 978-3-319-38798-7
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $89.99
price for Mexico
  • ISBN 978-3-319-38796-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $89.99
price for Mexico
  • ISBN 978-3-319-81748-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
The Congruences of a Finite Lattice
Book Subtitle
A "Proof-by-Picture" Approach
Authors
Copyright
2016
Publisher
Birkhäuser Basel
Copyright Holder
Springer International Publishing Switzerland
eBook ISBN
978-3-319-38798-7
DOI
10.1007/978-3-319-38798-7
Hardcover ISBN
978-3-319-38796-3
Softcover ISBN
978-3-319-81748-4
Edition Number
2
Number of Pages
XXXIV, 346
Number of Illustrations
159 b/w illustrations
Topics