Overview
- Offers a self-contained introduction to congruence lattices of finite lattices
- Presents major research results from the last 90 years
- Incorporates the author's signature "Proof-by-Picture" method
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Table of contents (29 chapters)
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A Brief Introduction to Lattices
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Some Special Techniques
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RTs
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ETs
Keywords
About this book
Key features include:
- an insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions
- complete proofs, an extensive bibliography and index, and over 180 illustrations
- additional chapters covering new results of the lastseven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references
This text is appropriate for a one-semester graduate course in lattice theory, and it will also serve as a valuable reference for researchers studying lattices.
Reviews of previous editions:
“[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. — Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica LII (1), 2007
"The book is self-contained, with many detailed proofs presented that can be followed step-by-step. 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
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/10.1007/978-3-031-29063-3
Publisher: Birkhäuser Cham
eBook Packages: Mathematics and Statistics, Mathematics and Statistics (R0)
Copyright Information: The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerland AG 2023
Hardcover ISBN: 978-3-031-29062-6Published: 24 March 2023
Softcover ISBN: 978-3-031-29065-7Published: 25 March 2024
eBook ISBN: 978-3-031-29063-3Published: 23 March 2023
Edition Number: 3
Number of Pages: XXXV, 430
Topics: Order, Lattices, Ordered Algebraic Structures, Group Theory and Generalizations, Convex and Discrete Geometry