The Congruences of a Finite Lattice [electronic resource] :A Proof-by-Picture Approach / by George Grätzer.
by Grätzer, George [author.]; SpringerLink (Online service).
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BookPublisher: Boston, MA : Birkhäuser Boston, 2006.Description: XXII, 282 p. 110 illus. online resource.ISBN: 9780817644628.Subject(s): Mathematics | Algebra | Logic, Symbolic and mathematical | Number theory | Distribution (Probability theory) | Mathematics | Order, Lattices, Ordered Algebraic Structures | Mathematical Logic and Foundations | Algebra | Probability Theory and Stochastic Processes | Number TheoryDDC classification: 511.33 Online resources: Click here to access online | Item type | Current location | Call number | Status | Date due | Barcode |
|---|---|---|---|---|---|
| QA171.5 (Browse shelf) | Available | ||||
| Long Loan | MAIN LIBRARY | QA172-172.4 (Browse shelf) | Available |
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| QA169 Categories and Commutative Algebra | QA169 Algebraic Operads | QA171.5 Ordered Sets | QA171.5 The Congruences of a Finite Lattice | QA171.5 Lattice-ordered Rings and Modules | QA171.5 Ensembles ordonnés finis : concepts, résultats et usages | QA171.5 Graph Theory in Paris |
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.
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.
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