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

The congruences of a lattice form the congruence lattice. Over the last several decades, the study of congruence lattices has established itself as a large and important field with a great number of interesting and deep results, as well as many open problems. Written by one of the leading experts in...

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Détails bibliographiques
Auteur principal: Grätzer, George (Auteur)
Collectivité auteur: SpringerLink (Online service)
Format: Électronique eBook
Langue:anglais
Publié: Cham : Springer International Publishing : Imprint: Birkhäuser, 2023.
Édition:3rd ed. 2023.
Sujets:
Algebra.
Group theory.
Convex geometry .
Discrete geometry.
Order, Lattices, Ordered Algebraic Structures.
Group Theory and Generalizations.
Convex and Discrete Geometry.
Accès en ligne:https://doi.org/10.1007/978-3-031-29063-3
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Table des matières:
  • Part I: A Brief Introduction to Lattices
  • Basic Concepts
  • Special Concepts
  • Congruences
  • Planar Semimodular Lattices
  • Part II: Some Special Techniques
  • Chopped Lattices
  • Boolean Triples
  • Cube Extensions
  • Part III: RTs
  • Sectionally Complemented RT
  • Minimal RT
  • Semimodular RT
  • Rectangular RT
  • Modular RT
  • Uniform RT
  • Part IV: ETs
  • Sectionally Complemented ET
  • Semimodular ET
  • Isoform ET
  • Magic Wands
  • Part V: Congruence Lattices of Two Related Lattices
  • Sublattices
  • Ideals
  • Two Convex Sublattices
  • Tensor Extensions
  • Part VI: The Ordered Set of Principle Congruences
  • The RT for Principal Congruences
  • Minimal RTs
  • Principal Congruence Representable Sets
  • Isotone Maps
  • Part VII: The Prime-Projectivity Lemma
  • The Swing Lemma
  • Fork Congruences
  • Part VIII: The Six Congruence Properties of SPS Lattices
  • Six Major Properties.

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