TY  - BOOK
AU  - Grätzer,George
ED  - SpringerLink (Online service)
TI  - The Congruences of a Finite Lattice: A Proof-by-Picture Approach 
SN  - 9780817644628
U1  - 511.33 23
PY  - 2006///
CY  - Boston, MA
PB  - Birkhäuser Boston
KW  - MATHEMATICS
KW  - ALGEBRA
KW  - LOGIC, SYMBOLIC AND MATHEMATICAL
KW  - NUMBER THEORY
KW  - DISTRIBUTION (PROBABILITY THEORY)
KW  - ORDER, LATTICES, ORDERED ALGEBRAIC STRUCTURES
KW  - MATHEMATICAL LOGIC AND FOUNDATIONS
KW  - PROBABILITY THEORY AND STOCHASTIC PROCESSES
N1  - 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
N2  - 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
UR  - http://dx.doi.org/10.1007/0-8176-4462-8
ER  -