2006

The Congruences of a Finite Lattice

A Proof-by-Picture Approach

Authors:

ISBN: 978-0-8176-3224-3 (Print) 978-0-8176-4462-8 (Online)

Table of contents (19 chapters)

  1. Front Matter

    Pages i-xxv

  2. A Brief Introduction to Lattices

    1. Front Matter

      Pages 1-1

    2. No Access

      Book Chapter

      Pages 3-17

      Basic Concepts

    3. No Access

      Book Chapter

      Pages 19-34

      Special Concepts

    4. No Access

      Book Chapter

      Pages 35-43

      Congruences

  3. Basic Techniques

    1. Front Matter

      Pages 45-45

    2. No Access

      Book Chapter

      Pages 47-55

      Chopped Lattices

    3. No Access

      Book Chapter

      Pages 57-69

      Boolean Triples

    4. No Access

      Book Chapter

      Pages 71-75

      Cubic Extensions

  4. Representation Theorems

    1. Front Matter

      Pages 77-77

    2. No Access

      Book Chapter

      Pages 79-91

      The Dilworth Theorem

    3. No Access

      Book Chapter

      Pages 93-103

      Minimal Representations

    4. No Access

      Book Chapter

      Pages 105-114

      Semimodular Lattices

    5. No Access

      Book Chapter

      Pages 115-127

      Modular Lattices

    6. No Access

      Book Chapter

      Pages 129-141

      Uniform Lattices

  5. Extensions

    1. Front Matter

      Pages 143-143

    2. No Access

      Book Chapter

      Pages 145-152

      Sectionally Complemented Lattices

    3. No Access

      Book Chapter

      Pages 153-160

      Semimodular Lattices

    4. No Access

      Book Chapter

      Pages 161-176

      Isoform Lattices

    5. No Access

      Book Chapter

      Pages 177-188

      Independence Theorems

    6. No Access

      Book Chapter

      Pages 189-211

      Magic Wands

  6. Two Lattices

    1. Front Matter

      Pages 213-213

    2. No Access

      Book Chapter

      Pages 215-226

      Sublattices

    3. No Access

      Book Chapter

      Pages 227-244

      Ideals

    4. No Access

      Book Chapter

      Pages 245-264

      Tensor Extensions

  7. Back Matter

    Pages 265-281