{"product_id":"theory-of-symmetric-lattices-von-fumitomo-maeda-shuichiro-maeda","title":"Theory of Symmetric Lattices","description":"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.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783642462504\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Libri","offers":[{"title":"Softcover - 9783642462504","offer_id":39426649129053,"sku":"9783642462504","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/a43fe1b3-5af1-4013-90f2-9b59cbcb7c02.jpg?v=1772084896","url":"https:\/\/shop.autorenwelt.de\/products\/theory-of-symmetric-lattices-von-fumitomo-maeda-shuichiro-maeda","provider":"Autorenwelt Shop","version":"1.0","type":"link"}