Semimodular Lattices

Theory and Applications

By: Manfred Stern, Stern Manfred

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Paperback | 3 September 2009

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388 Pages

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Lattice theory evolved as part of algebra in the nineteenth century through the work of Boole, Peirce and Schroder, and in the first half of the twentieth century through the work of Dedekind, Birkhoff, Ore, von Neumann, Mac Lane, Wilcox, Dilworth, and others. In Semimodular Lattices, 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 author surveys and analyzes Birkhoff's concept of semimodularity and the various related concepts in lattice theory, and he presents theoretical results as well as applications in discrete mathematics group theory and universal algebra. Special emphasis is given to the combinatorial aspects of finite semimodular lattices and to the connections between matroids and geometric lattices, antimatroids and locally distributive lattices. The book also deals with lattices that are "close" to semimodularity or can be combined with semimodularity, for example supersolvable, admissible, consistent, strong, and balanced lattices. Researchers in lattice theory, discrete mathematics, combinatorics, and algebra will find this book valuable.

Industry Reviews

'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

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You Can Find This Book In

Non-Fiction Mathematics Topology Combinatorics & Graph Theory Algebra Mathematical Foundation Mathematical Logic

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Hardcover

Published: 13th September 1999

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Preface
From Boolean algebras to semimodular lattices
M-symmetric lattices
Conditions related to semimodularity, 0-conditions and disjointness properties
Supersolvable and admissible lattices, consistent and strong lattices
The covering graph
Semimodular lattices of finite length
Local distributivity
Local modularity
Congruence semimodularity
Master reference list
Table of notation
Index
Table of Contents provided by Publisher. All Rights Reserved.

Semimodular Lattices

Theory and Applications

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

Other Editions and Formats

Hardcover

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