Cover Image
Read Now

The Congruences of a Finite Lattice A "Proof-by-Picture" Approach

This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method. Key features: * Insightful discussion of te...

Full description

Bibliographic Details
Main Author: Grätzer, George
Format: eBook
Language:English
Published: Cham Birkhäuser 2016, 2016
Edition:2nd ed. 2016
Subjects:
Number Theory
Mathematical Logic
Probability Theory
Algebra
Order, Lattices, Ordered Algebraic Structures
Mathematical Logic And Foundations
Probabilities
Online Access:
Collection: Springer eBooks 2005- - Collection details see MPG.ReNa
Table of Contents:
  • I: A Brief Introduction to Lattices
  • Basic Concepts
  • Special Concepts
  • Congruences
  • Planar Semimodular Lattices
  • II: Some Special Techniques
  • Chopped Lattices
  • Boolean Triples
  • Cubic Extensions
  • III: Congruence Lattices of Finite Lattices
  • The Dilworth Theorem
  • Minimal Representations
  • Semimodular Lattices
  • Rectangular Lattices
  • Modular Lattices
  • Uniform Lattices
  • IV: Congruence Lattices and Lattice Extensions
  • Sectionally Complemented Lattices
  • Semimodular Lattices
  • Isoform Lattices
  • The Congruence Lattice and the Automorphism Group
  • Magic Wands
  • V: Congruence Lattices of Two Related Lattices
  • Sublattices
  • Ideals
  • Tensor Extensions
  • VI The Ordered Set of Principal Congruences
  • Representation Theorems
  • Isotone Maps
  • VII: Congruence Structure
  • Prime Intervals and Congruences
  • Some Applications of the Swing Lemma

Similar Items