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)
Download Book (2,228 KB) As a courtesy to our readers the eBook is provided DRM-free. However, please note that Springer uses effective methods and state-of-the art technology to detect, stop, and prosecute illegal sharing to safeguard our authors’ interests.

Table of contents (19 chapters)

  1. A Brief Introduction to Lattices

    1. Front Matter

      Pages 1-1

    2. Book Chapter

      Pages 3-17

      Basic Concepts

    3. Book Chapter

      Pages 19-34

      Special Concepts

    4. Book Chapter

      Pages 35-43

      Congruences

  2. Basic Techniques

    1. Front Matter

      Pages 45-45

    2. Book Chapter

      Pages 47-55

      Chopped Lattices

    3. Book Chapter

      Pages 57-69

      Boolean Triples

    4. Book Chapter

      Pages 71-75

      Cubic Extensions

  3. Representation Theorems

    1. Front Matter

      Pages 77-77

    2. Book Chapter

      Pages 79-91

      The Dilworth Theorem

    3. Book Chapter

      Pages 93-103

      Minimal Representations

    4. Book Chapter

      Pages 105-114

      Semimodular Lattices

    5. Book Chapter

      Pages 115-127

      Modular Lattices

    6. Book Chapter

      Pages 129-141

      Uniform Lattices

  4. Extensions

    1. Front Matter

      Pages 143-143

    2. Book Chapter

      Pages 145-152

      Sectionally Complemented Lattices

    3. Book Chapter

      Pages 153-160

      Semimodular Lattices

    4. Book Chapter

      Pages 161-176

      Isoform Lattices

    5. Book Chapter

      Pages 177-188

      Independence Theorems

    6. Book Chapter

      Pages 189-211

      Magic Wands

  5. Two Lattices

    1. Front Matter

      Pages 213-213

    2. Book Chapter

      Pages 215-226

      Sublattices

    3. Book Chapter

      Pages 227-244

      Ideals

    4. Book Chapter

      Pages 245-264

      Tensor Extensions