Semimodular Lattices
Theory and Applications

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

Manfred Stern (Author)

9780521118842, Cambridge University Press

Paperback, published 3 September 2009

388 pages
22.9 x 15.2 x 2 cm, 0.57 kg

'… a very well organized book … a pleasure to read … will certainly become a standard source.' Horst Szambien, Zentralblatt MATH

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.

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.

Subject Areas: Mathematical foundations [PBC]