# The Congruences of a Finite Lattice

## A "Proof-by-Picture" Approach

- 10 Citations
- 4 Mentions
- 12k Downloads

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Textbook

- 10 Citations
- 4 Mentions
- 12k Downloads

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)**

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Lattices Congruence Boolean Triples Minimal Representation Automorphism Group Principal Congruences Prime Interval

- DOI https://doi.org/10.1007/978-3-319-38798-7
- Copyright Information Springer International Publishing Switzerland 2016
- Publisher Name Birkhäuser, Cham
- eBook Packages Mathematics and Statistics
- Print ISBN 978-3-319-38796-3
- Online ISBN 978-3-319-38798-7
- Buy this book on publisher's site