Theory of Symmetric Lattices is popular PDF and ePub book, written by Fumitomo Maeda in 2012-12-06, it is a fantastic choice for those who relish reading online the Mathematics genre. Let's immerse ourselves in this engaging Mathematics book by exploring the summary and details provided below. Remember, Theory of Symmetric Lattices can be Read Online from any device for your convenience.
Theory of Symmetric Lattices Book PDF Summary
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.
Detail Book of Theory of Symmetric Lattices PDF
- Author : Fumitomo Maeda
- Release : 06 December 2012
- Publisher : Springer Science & Business Media
- ISBN : 9783642462481
- Genre : Mathematics
- Total Page : 204 pages
- Language : English
- PDF File Size : 8,7 Mb
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