Theory of Symmetric Lattices:
Saved in:
| Main Author: | |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Berlin, Heidelberg
Springer Berlin Heidelberg
1970
|
| Series: | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete
173 |
| Subjects: | |
| Online Access: | Volltext |
| Item 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 |
| Physical Description: | 1 Online-Ressource (XII, 194 p) |
| ISBN: | 9783642462481 9783642462504 |
| ISSN: | 0072-7830 |
| DOI: | 10.1007/978-3-642-46248-1 |
Staff View
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| 500 | |a 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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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
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| discipline | Mathematik |
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| illustrated | Not Illustrated |
| indexdate | 2024-07-10T01:21:11Z |
| institution | BVB |
| isbn | 9783642462481 9783642462504 |
| issn | 0072-7830 |
| language | English |
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| physical | 1 Online-Ressource (XII, 194 p) |
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| publishDate | 1970 |
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| series2 | Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete |
| spelling | Maeda, Fumitomo Verfasser aut Theory of Symmetric Lattices by Fumitomo Maeda, Shûichirô Maeda Berlin, Heidelberg Springer Berlin Heidelberg 1970 1 Online-Ressource (XII, 194 p) txt rdacontent c rdamedia cr rdacarrier Die Grundlehren der mathematischen Wissenschaften, in Einzeldarstellungen mit besonderer Berücksichtigung der Anwendungsgebiete 173 0072-7830 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 Mathematics Mathematics, general Mathematik Symmetrie (DE-588)4058724-1 gnd rswk-swf Verbandstheorie (DE-588)4127072-1 gnd rswk-swf Gitter Mathematik (DE-588)4157375-4 gnd rswk-swf Symmetrie (DE-588)4058724-1 s Verbandstheorie (DE-588)4127072-1 s 1\p DE-604 Gitter Mathematik (DE-588)4157375-4 s 2\p DE-604 Maeda, Shûichirô Sonstige oth https://doi.org/10.1007/978-3-642-46248-1 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Maeda, Fumitomo Theory of Symmetric Lattices Mathematics Mathematics, general Mathematik Symmetrie (DE-588)4058724-1 gnd Verbandstheorie (DE-588)4127072-1 gnd Gitter Mathematik (DE-588)4157375-4 gnd |
| subject_GND | (DE-588)4058724-1 (DE-588)4127072-1 (DE-588)4157375-4 |
| title | Theory of Symmetric Lattices |
| title_auth | Theory of Symmetric Lattices |
| title_exact_search | Theory of Symmetric Lattices |
| title_full | Theory of Symmetric Lattices by Fumitomo Maeda, Shûichirô Maeda |
| title_fullStr | Theory of Symmetric Lattices by Fumitomo Maeda, Shûichirô Maeda |
| title_full_unstemmed | Theory of Symmetric Lattices by Fumitomo Maeda, Shûichirô Maeda |
| title_short | Theory of Symmetric Lattices |
| title_sort | theory of symmetric lattices |
| topic | Mathematics Mathematics, general Mathematik Symmetrie (DE-588)4058724-1 gnd Verbandstheorie (DE-588)4127072-1 gnd Gitter Mathematik (DE-588)4157375-4 gnd |
| topic_facet | Mathematics Mathematics, general Mathematik Symmetrie Verbandstheorie Gitter Mathematik |
| url | https://doi.org/10.1007/978-3-642-46248-1 |
| work_keys_str_mv | AT maedafumitomo theoryofsymmetriclattices AT maedashuichiro theoryofsymmetriclattices |