Semimodular Lattices
Semimodular Lattices
In Semimodular Lattices: Theory and Applications Manfred Stern uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. He focuses on the important theory of semimodularity, its many ramifications, and its applications in discrete mathematics, combinatorics, and algebra. The book surveys and analyzes Garrett Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and it presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. The author also deals with lattices that are 'close' to semimodularity or can be combined with semimodularity, e.g. supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book invaluable.
- Introduces the theory of semimodular lattices as a far-reaching generalization of Boolean algebras
- Examines the interdependence of related concepts such as M-symmetry and conditions of MacLane and Dilworth
- Has applications to discrete mathematics, combinatorics, group theory and universal algebra
Reviews & endorsements
'Researchers working in lattice theory will surely welcome this excellent and up-to-date reference book.' Acta. Sci. Math.
'I recommend the book highly to all interested readers, both experts and non-experts.' Stefan E. Schmidt, Bulletin of the London Mathematical Society
'… a very well organized book … a pleasure to read … will certainly become a standard source.' Horst Szambien, Zentralblatt MATH
Product details
April 2011Adobe eBook Reader
9780511834561
0 pages
0kg
This ISBN is for an eBook version which is distributed on our behalf by a third party.
Table of Contents
- Preface
- 1. From Boolean algebras to semimodular lattices
- 2. M-symmetric lattices
- 3. Conditions related to semimodularity, 0-conditions and disjointness properties
- 4. Supersolvable and admissible lattices, consistent and strong lattices
- 5. The covering graph
- 6. Semimodular lattices of finite length
- 7. Local distributivity
- 8. Local modularity
- 9. Congruence semimodularity
- Master reference list
- Table of notation
- Index.
