Semimodular Lattices
Theory and Applications
1st Edition
Published on 4. April 2011
978-0-511-83456-1 (ISBN)
Description
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.
Reviews / Votes
'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 MATHMore details
Series
Language
English
Place of publication
Cambridge
United Kingdom
Publishing group
Cambridge University Press
Target group
Professional and scholarly
Illustrations
Worked examples or Exercises
File size
25,07 MB
ISBN-13
978-0-511-83456-1 (9780511834561)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Book
09/2009
Cambridge University Press
€77.20
Shipment within 15-20 days
Book
05/1999
Cambridge University Press
€173.60
Shipment within 15-20 days
Content
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.
