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The Congruences of a Finite Lattice: A Proof-By-Picture Approach
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AlgebraGeneral MathematicsGeometry
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ISBN10: 3031290658
ISBN13: 9783031290657
Publisher: Birkhauser
Published: Mar 25 2024
Pages: 430
Language: English
ISBN13: 9783031290657
Publisher: Birkhauser
Published: Mar 25 2024
Pages: 430
Language: English
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:
[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
- 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] 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
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