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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Theory of Symmetric Lattices

Theory of Symmetric Lattices

Maeda, Fumitomo
Maeda, Shuichiro

Paperback

Series: Grundlehren Der Mathematischen Wissenschaften, Book 173

Algebra

ISBN10: 3642462502
ISBN13: 9783642462504
Publisher: Springer Nature
Published: Mar 17 2012
Pages: 194
Weight: 0.67
Height: 0.45 Width: 6.14 Depth: 9.21
Language: English
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.

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