The Congruences of a Finite Lattice : A Proof-by-Picture Approach / by George Grätzer.

Springer eBooks

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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