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

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

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...

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Bibliographic Details
Main Author: Grätzer, George (Author)
Corporate Author: SpringerLink (Online service)
Format: eBook
Language:English
Published: Cham : Springer International Publishing : Imprint: Birkhäuser, 2016.
Edition:2nd ed. 2016.
Series:Springer eBook Collection.
Subjects:
Algebra.
Ordered algebraic structures.
Mathematical logic.
Probabilities.
Number theory.
Electronic resources (E-books)
Online Access:Click to view e-book
Holy Cross Note:Loaded electronically.
Electronic access restricted to members of the Holy Cross Community.
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.

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