Theory of Symmetric Lattices (Paperback, Softcover reprint of the original 1st ed. 1970)

Of central importance in this book is the concept of modularity in lattices. A lattice is said to be modular if every pair of its elements is a modular pair. The properties of modular lattices have been carefully investigated by numerous mathematicians, including 1. von Neumann who introduced the important study of continuous geometry. Continu ous geometry is a generalization of projective geometry; the latter is atomistic and discrete dimensional while the former may include a continuous dimensional part. Meanwhile there are many non-modular lattices. Among these there exist some lattices wherein modularity is symmetric, that is, if a pair (a, b) is modular then so is (b, a). These lattices are said to be M-sym metric, and their study forms an extension of the theory of modular lattices. An important example of an M-symmetric lattice arises from affine geometry. Here the lattice of affine sets is upper continuous, atomistic, and has the covering property. Such a lattice, called a matroid lattice, can be shown to be M-symmetric. We have a deep theory of parallelism in an affine matroid lattice, a special kind of matroid lattice. Further more we can show that this lattice has a modular extension."

General

Imprint:	Springer-Verlag
Country of origin:	Germany
Series:	Grundlehren der mathematischen Wissenschaften, 173
Release date:	March 2012
First published:	1970
Authors:	Fumitomo Maeda • Shuichiro Maeda
Dimensions:	235 x 155 x 11mm (L x W x T)
Format:	Paperback
Pages:	194
Edition:	Softcover reprint of the original 1st ed. 1970
ISBN-13:	978-3-642-46250-4
Categories:	Books > Science & Mathematics > Mathematics > Algebra > General
LSN:	3-642-46250-2
Barcode:	9783642462504

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