Semimodular Lattices : Theory and Applications /

A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Stern, Manfred
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Cambridge : Cambridge University Press, 1999.
Colección:Encyclopedia of mathematics and its applications ; no. 73.
Temas:
Semimodular lattices.
Treillis semi-modulaires.
MATHEMATICS > General.
Semimodular lattices
Acceso en línea:Texto completo
Tabla de Contenidos:
  • Cover
  • Title
  • Copyright
  • Contents
  • Preface
  • 1 From Boolean Algebras to Semimodular Lattices
  • 1.1 Sources of Semimodularity
  • Boolean Algebras and Distributive Lattices
  • Modular Lattices
  • Semimodular Lattices
  • Conditions Related to Semimodularity
  • Local Distributivity and Local Modularity
  • Notes
  • References
  • 1.2 Boolean Lattices, Ortholattices, and Orthomodular Lattices
  • Notes
  • References
  • 1.3 Distributive and Semidistributive Lattices
  • Notes
  • References
  • 1.4 Pseudocomplemented Lattices
  • References
  • 1.5 Complementation
  • Notes
  • References.
  • 1.6 Modular Lattices
  • Notes
  • References
  • 1.7 Upper and Lower Semimodularity
  • Notes
  • Exercises
  • References
  • 1.8 Existence of Decompositions
  • Notes
  • Exercises
  • References
  • 1.9 The Jordan-Dedekind Chain Condition
  • Notes
  • Exercises
  • References
  • 2 M-Symmetric Lattices
  • 2.1 Modular Pairs and Modular Elements
  • Notes
  • Exercises
  • References
  • 2.2 Distributive, Standard, and Neutral Elements
  • Notes
  • Exercises
  • References
  • 2.3 M-Symmetry and Related Concepts
  • Notes
  • Exercises
  • References
  • 2.4 Wilcox Lattices
  • Notes
  • Exercises
  • References.
  • 2.5 Finite-Modular and Weakly Modular AC Lattices
  • Notes
  • Exercises
  • References
  • 2.6 Orthomodular M-Symmetric Lattices
  • Notes
  • Exercises
  • References
  • 3 Conditions Related to Semimodularity, O-Conditions, and Disjointness Properties
  • 3.1 Mac Lane's Condition
  • Notes
  • Exercises
  • References
  • 3.2 Conditions for the Ideal Lattice
  • Notes
  • Exercises
  • References
  • 3.3 Interrelationships in Lattices with a Chain Condition
  • Notes
  • Exercises
  • References
  • 3.4 0-Conditions and Disjointness Properties
  • Notes
  • Exercises
  • References.
  • 3.5 Interrelationships in Lattices with Complementation
  • Exercises
  • References
  • 4 Supersolvable and Admissible Lattices
  • Consistent and Strong Lattices
  • 4.1 The Mobius Function
  • Notes
  • Exercises
  • References
  • 4.2 Complements and Fixed Points
  • Notes
  • Exercises
  • References
  • 4.3 Supersolvable Lattices
  • Notes
  • Exercises
  • References
  • 4.4 Admissible Lattices and Cohen-Macaulay Posets
  • Notes
  • Exercises
  • References
  • 4.5 Consistent Lattices
  • Notes
  • Exercises
  • References
  • 4.6 Strong Lattices and Balanced Lattices
  • Notes
  • Exercises
  • References.
  • 5 The Covering Graph
  • 5.1 Diagrams and Covering Graphs
  • Notes
  • References
  • 5.2 Path Length
  • Notes
  • Exercises
  • References
  • 5.3 Graph Isomorphisms of Graded Balanced Lattices
  • Notes
  • Exercises
  • References
  • 5.4 Semimodular Lattices with Isomorphic Covering Graphs
  • Notes
  • References
  • 5.5 Centrally Symmetric Graphs and Lattices
  • Notes
  • Exercises
  • References
  • 5.6 Subgraphs of the Covering Graph
  • Notes
  • Exercises
  • References
  • 6 Semimodular Lattices of Finite Length
  • 6.1 Rank and Covering Inequalities
  • Notes
  • Exercises
  • References
  • 6.2 Embeddings.

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