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Semimodular Lattices: Theory and Applications: 73 (Encyclopedia of Mathematics and its Applications, Series Number 73) - Hardcover
Synopsis
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.
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Review
'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
Book Description
Semimodular Lattices: Theory and Applications uses successive generalizations of distributive and modular lattices to outline the development of semimodular lattices from Boolean algebras. It surveys and analyzes Garrett Birkhoff's concept of semimodularity, and he presents theoretical results as well as applications in discrete mathematics, group theory and universal algebra.
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