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EBOOK
Author Stern, Manfred.
Title Semimodular Lattices : Theory and Applications / Manfred Stern.
Imprint Cambridge : Cambridge University Press, 1999.

Author Stern, Manfred.
Series Encyclopedia of Mathematics and its Applications ; no. 73
Encyclopedia of mathematics and its applications ; no. 73.
Subject Semimodular lattices.
Author Stern, Manfred.
Series Encyclopedia of Mathematics and its Applications ; no. 73
Encyclopedia of mathematics and its applications ; no. 73.
Subject Semimodular lattices.
Description 1 online resource (388 pages)
Note Print version record.
Title from publishers bibliographic system (viewed 22 Dec 2011).
Summary A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
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.
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.
ISBN 9781107088702 (electronic bk.)
1107088704 (electronic bk.)
9780511665578 (electronic bk.)
0511665571 (electronic bk.)
9781107094932
1107094933
9780521118842 (paperback)
0521118840
9780521461054 (hardback)
0521461057 (hardback)
OCLC # 776957870
Additional Format Print version: Stern, Manfred. Semimodular Lattices. Cambridge : Cambridge University Press, 1999 9780511665578


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