The congruences of a finite lattice : a "proof-by-picture" approach / George Grätzer.
Gratzer, George A., author.
2023
QA171.5
Available Online

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Title The congruences of a finite lattice : a "proof-by-picture" approach / George Grätzer.
Author Gratzer, George A., author.
Edition Third edition.
ISBN 9783031290633 (electronic bk.)
3031290631 (electronic bk.)
9783031290626 (print)
3031290623
DOI https://doi.org/10.1007/978-3-031-29063-3
Published Cham : Birkhäuser, 2023.
Language English
Description 1 online resource (xxxv, 430 pages)
Other Standard Identifiers 10.1007/978-3-031-29063-3 doi
Call Number QA171.5
Dewey Decimal Classification 511.3/3
Summary The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in lattice theory, this text provides a self-contained introduction to congruences of finite lattices and presents the major results of the last 90 years. It features the author’s signature "Proof-by-Picture" method, which is used to convey the ideas behind formal proofs in a visual, more intuitive manner. 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 last seven years, increasing the size of this edition to 430 pages, 360 statements, and 262 references
Bibliography, etc. Note Includes bibliographical references and index.
Access Note Access limited to authorized users.
Source of Description Online resource; title from PDF title page (SpringerLink, viewed March 30, 2023).
Available in Other Form Print version: 9783031290626
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Part I: A Brief Introduction to Lattices
Basic Concepts
Special Concepts
Congruences
Planar Semimodular Lattices
Part II: Some Special Techniques
Chopped Lattices
Boolean Triples
Cube Extensions
Part III: RTs
Sectionally Complemented RT
Minimal RT
Semimodular RT
Rectangular RT
Modular RT
Uniform RT
Part IV: ETs
Sectionally Complemented ET
Semimodular ET
Isoform ET
Magic Wands
Part V: Congruence Lattices of Two Related Lattices
Sublattices
Ideals
Two Convex Sublattices
Tensor Extensions
Part VI: The Ordered Set of Principle Congruences
The RT for Principal Congruences
Minimal RTs
Principal Congruence Representable Sets
Isotone Maps
Part VII: The Prime-Projectivity Lemma
The Swing Lemma
Fork Congruences
Part VIII: The Six Congruence Properties of SPS Lattices
Six Major Properties.

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