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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| Format: | eBook |
| Language: | English |
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Cham
Birkhäuser
2023, 2023
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| Edition: | 3rd ed. 2023 |
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| Online Access: | |
| Collection: | Springer eBooks 2005- - Collection details see MPG.ReNa |
Table of Contents:
- 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