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
"Professor Stern's book is the first to include the latest developments in the theory of semimodular lattices. His clear presentation, and his readable mathematical style, will make his treatise an indispensable vade mecum for lattice theorists, and for all discrete mathematicians everywhere." Mathematical Reviews
Product details
May 1999Hardback
9780521461054
388 pages
244 × 162 × 28 mm
0.725kg
Available
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.
