| Description |
1 online resource (388 pages) |
| Series |
Encyclopedia of Mathematics and its Applications ; no. 73 |
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Encyclopedia of mathematics and its applications ; no. 73.
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| Contents |
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 |
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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 |
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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 |
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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 |
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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 |
| Summary |
A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra |
| Notes |
Title from publishers bibliographic system (viewed 22 Dec 2011) |
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Print version record |
| Subject |
Semimodular lattices.
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MATHEMATICS -- General.
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Semimodular lattices
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| Form |
Electronic book
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| ISBN |
9781107088702 |
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1107088704 |
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9780511665578 |
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0511665571 |
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9781107094932 |
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1107094933 |
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9780521118842 |
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0521118840 |
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