| Description |
1 online resource (xxii, 281 pages) : illustrations |
| Contents |
A Brief Introduction to Lattices -- Basic Concepts -- Special Concepts -- Congruences -- Basic Techniques -- Chopped Lattices -- Boolean Triples -- Cubic Extensions -- Representation Theorems -- The Dilworth Theorem -- Minimal Representations -- Semimodular Lattices -- Modular Lattices -- Uniform Lattices -- Extensions -- Sectionally Complemented Lattices -- Semimodular Lattices -- Isoform Lattices -- Independence Theorems -- Magic Wands -- Two Lattices -- Sublattices -- Ideals -- Tensor Extensions |
| Summary |
The congruences of a lattice form the congruence lattice. In the past half-century, the study of congruence lattices has become a large and important field with a great number of interesting and deep results and many open problems. This self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presents the major results on congruence lattices of finite lattices featuring the author's signature "Proof-by-Picture" method and its conversion to transparencies. Key features: * Includes the latest findings from a pioneering researcher in the field * 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 nearly 80 open problems * Additional information provided by the author online at: http://www.maths.umanitoba.ca/homepages/gratzer.html/ The book is appropriate for a one-semester graduate course in lattice theory, yet is also designed as a practical reference for researchers studying lattices |
| Bibliography |
Includes bibliographical references (pages 265-273) and index |
| Notes |
English |
|
Print version record |
| In |
Springer e-books |
| Subject |
Congruence lattices.
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Lattice theory.
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Algebra.
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Distribution (Probability theory)
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algebra.
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distribution (statistics-related concept)
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Lattice theory.
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Treillis de congruences.
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Treillis, Théorie des.
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Congruence lattices.
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Distribución (Teoría de probabilidades)
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Retículos, Teoría de
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Congruence lattices
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Lattice theory
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| Form |
Electronic book
|
| LC no. |
2005934394 |
| ISBN |
9780817644628 |
|
0817644628 |
|
0817632247 |
|
9780817632243 |
|
1281335592 |
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9781281335593 |
|
