| 书目名称 | Theory of Symmetric Lattices | | 编辑 | Fumitomo Maeda,Shûichirô Maeda | | 视频video | | | 丛书名称 | Grundlehren der mathematischen Wissenschaften | | 图书封面 |  | | 描述 | 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 mod | | 出版日期 | Book 19701st edition | | 关键词 | Finite; Lattice; Lattices; Verband; duality; eXist; form; geometry; matroid; modularity; parallelism; projectiv | | 版次 | 1 | | doi | https://doi.org/10.1007/978-3-642-46248-1 | | isbn_softcover | 978-3-642-46250-4 | | isbn_ebook | 978-3-642-46248-1Series ISSN 0072-7830 Series E-ISSN 2196-9701 | | issn_series | 0072-7830 | | copyright | Springer-Verlag Berlin · Heidelberg 1970 |
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发表于 2025-3-21 16:37:20
