F. Maeda [and] S. Maeda ;Theory of Symmetric Lattices
Author | : S. Maeda |
Publisher | : |
Total Pages | : 190 |
Release | : 1970 |
Genre | : |
ISBN | : |
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Author | : S. Maeda |
Publisher | : |
Total Pages | : 190 |
Release | : 1970 |
Genre | : |
ISBN | : |
Author | : Fumitomo Maeda |
Publisher | : Springer Science & Business Media |
Total Pages | : 204 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 3642462480 |
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.
Author | : Fumitomo Maeda |
Publisher | : |
Total Pages | : 201 |
Release | : 1970 |
Genre | : |
ISBN | : |
Author | : |
Publisher | : Springer-Verlag |
Total Pages | : 237 |
Release | : 2013-12-01 |
Genre | : Technology & Engineering |
ISBN | : 3663124789 |
Author | : Shūichirō Maeda |
Publisher | : |
Total Pages | : 596 |
Release | : 1968 |
Genre | : Lattice theory |
ISBN | : |
Author | : George Grätzer |
Publisher | : Springer Science & Business Media |
Total Pages | : 639 |
Release | : 2011-02-14 |
Genre | : Mathematics |
ISBN | : 3034800185 |
This book started with Lattice Theory, First Concepts, in 1971. Then came General Lattice Theory, First Edition, in 1978, and the Second Edition twenty years later. Since the publication of the first edition in 1978, General Lattice Theory has become the authoritative introduction to lattice theory for graduate students and the standard reference for researchers. The First Edition set out to introduce and survey lattice theory. Some 12,000 papers have been published in the field since then; so Lattice Theory: Foundation focuses on introducing the field, laying the foundation for special topics and applications. Lattice Theory: Foundation, based on the previous three books, covers the fundamental concepts and results. The main topics are distributivity, congruences, constructions, modularity and semimodularity, varieties, and free products. The chapter on constructions is new, all the other chapters are revised and expanded versions from the earlier volumes. Almost 40 “diamond sections’’, many written by leading specialists in these fields, provide a brief glimpse into special topics beyond the basics. “Lattice theory has come a long way... For those who appreciate lattice theory, or who are curious about its techniques and intriguing internal problems, Professor Grätzer's lucid new book provides a most valuable guide to many recent developments. Even a cursory reading should provide those few who may still believe that lattice theory is superficial or naive, with convincing evidence of its technical depth and sophistication.” Bulletin of the American Mathematical Society “Grätzer’s book General Lattice Theory has become the lattice theorist’s bible.” Mathematical Reviews
Author | : Library of Congress. Copyright Office |
Publisher | : Copyright Office, Library of Congress |
Total Pages | : 1642 |
Release | : 1973 |
Genre | : Copyright |
ISBN | : |
Author | : |
Publisher | : |
Total Pages | : 224 |
Release | : 1973-04 |
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ISBN | : |
Author | : Ivan Rival |
Publisher | : Springer Science & Business Media |
Total Pages | : 963 |
Release | : 2012-12-06 |
Genre | : Computers |
ISBN | : 9400977980 |
This volume contains all twenty-three of the principal survey papers presented at the Symposium on Ordered Sets held at Banff, Canada from August 28 to September 12, 1981. The Symposium was supported by grants from the NATO Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada, the Canadian Mathematical Society Summer Research Institute programme, and the University of Calgary. tve are very grateful to these Organizations for their considerable interest and support. Over forty years ago on April 15, 1938 the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. in conjunction with a meeting of the American Mathematical Society. The principal addresses on that occasion were Lattices and their applications by G. Birkhoff, On the application of structure theory to groups by O. Ore, and The representation of Boolean algebras by M. H. Stone. The texts of these addresses and three others by R. Baer, H. M. MacNeille, and K. Menger appear in the Bulletin of the American Mathematical Society, Volume 44, 1938. In those days the theory of ordered sets, and especially lattice theory was described as a "vigorous and promising younger brother of group theory." Some early workers hoped that lattice theoretic methods would lead to solutions of important problems in group theory.
Author | : Sterling K. Berberian |
Publisher | : Springer Science & Business Media |
Total Pages | : 309 |
Release | : 2010-10-27 |
Genre | : Mathematics |
ISBN | : 3642150713 |
A systematic exposition of Baer *-Rings, with emphasis on the ring-theoretic and lattice-theoretic foundations of von Neumann algebras. Equivalence of projections, decompositio into types; connections with AW*-algebras, *-regular rings, continuous geometries. Special topics include the theory of finite Baer *-rings (dimension theory, reduction theory, embedding in *-regular rings) and matrix rings over Baer *-rings. Written to be used as a textbook as well as a reference, the book includes more than 400 exercises, accompanied by notes, hints, and references to the literature. Errata and comments from the author have been added at the end of the present reprint (2nd printing 2010).