Ordered Sets And Lattices Ii
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Ordered Sets And Lattices Ii
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Author :
language : en
Publisher: American Mathematical Soc.
Release Date :
Ordered Sets And Lattices Ii written by and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on with categories.
This indispensable reference source contains a wealth of information on lattice theory. The book presents a survey of virtually everything published in the fields of partially ordered sets, semilattices, lattices, and Boolean algebras that was reviewed in Referativnyi Zhurnal Matematika from mid-1982 to the end of 1985. A continuation of a previous volume (the English translation of which was published by the AMS in 1989, as volume 141 in Translations - Series 2), this comprehensive work contains more than 2200 references. Many of the papers covered here were originally published in virtually inaccessible places. The compilation of the volume was directed by Milan Kolibiar of Comenius University at Bratislava and Lev A. Skornyakov of Moscow University. Of interest to mathematicians, as well as to philosophers and computer scientists in certain areas, this unique compendium is a must for any mathematical library.
Lattices And Ordered Sets
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Author : Steven Roman
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15
Lattices And Ordered Sets written by Steven Roman and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-12-15 with Mathematics categories.
This book is intended to be a thorough introduction to the subject of order and lattices, with an emphasis on the latter. It can be used for a course at the graduate or advanced undergraduate level or for independent study. Prerequisites are kept to a minimum, but an introductory course in abstract algebra is highly recommended, since many of the examples are drawn from this area. This is a book on pure mathematics: I do not discuss the applications of lattice theory to physics, computer science or other disciplines. Lattice theory began in the early 1890s, when Richard Dedekind wanted to know the answer to the following question: Given three subgroups EF , and G of an abelian group K, what is the largest number of distinct subgroups that can be formed using these subgroups and the operations of intersection and sum (join), as in E?FßÐE?FÑ?GßE?ÐF?GÑ and so on? In lattice-theoretic terms, this is the number of elements in the relatively free modular lattice on three generators. Dedekind [15] answered this question (the answer is #)) and wrote two papers on the subject of lattice theory, but then the subject lay relatively dormant until Garrett Birkhoff, Oystein Ore and others picked it up in the 1930s. Since then, many noted mathematicians have contributed to the subject, including Garrett Birkhoff, Richard Dedekind, Israel Gelfand, George Grätzer, Aleksandr Kurosh, Anatoly Malcev, Oystein Ore, Gian-Carlo Rota, Alfred Tarski and Johnny von Neumann.
Introduction To Lattices And Order
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Author : B. A. Davey
language : en
Publisher: Cambridge University Press
Release Date : 2002-04-18
Introduction To Lattices And Order written by B. A. Davey and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-04-18 with Mathematics categories.
This new edition of Introduction to Lattices and Order presents a radical reorganization and updating, though its primary aim is unchanged. The explosive development of theoretical computer science in recent years has, in particular, influenced the book's evolution: a fresh treatment of fixpoints testifies to this and Galois connections now feature prominently. An early presentation of concept analysis gives both a concrete foundation for the subsequent theory of complete lattices and a glimpse of a methodology for data analysis that is of commercial value in social science. Classroom experience has led to numerous pedagogical improvements and many new exercises have been added. As before, exposure to elementary abstract algebra and the notation of set theory are the only prerequisites, making the book suitable for advanced undergraduates and beginning graduate students. It will also be a valuable resource for anyone who meets ordered structures.
Lattices And Ordered Algebraic Structures
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Author : T.S. Blyth
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-04-18
Lattices And Ordered Algebraic Structures written by T.S. Blyth and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005-04-18 with Mathematics categories.
"The text can serve as an introduction to fundamentals in the respective areas from a residuated-maps perspective and with an eye on coordinatization. The historical notes that are interspersed are also worth mentioning....The exposition is thorough and all proofs that the reviewer checked were highly polished....Overall, the book is a well-done introduction from a distinct point of view and with exposure to the author’s research expertise." --MATHEMATICAL REVIEWS
Ordered Sets
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Author : Bernd Schröder
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ordered Sets written by Bernd Schröder and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
This work is an introduction to the basic tools of the theory of (partially) ordered sets such as visualization via diagrams, subsets, homomorphisms, important order-theoretical constructions, and classes of ordered sets. Using a thematic approach, the author presents open or recently solved problems to motivate the development of constructions and investigations for new classes of ordered sets. A wide range of material is presented, from classical results such as Dilworth's, Szpilrajn's and Hashimoto's Theorems to more recent results such as the Li--Milner Structure Theorem. Major topics covered include: chains and antichains, lowest upper and greatest lower bounds, retractions, lattices, the dimension of ordered sets, interval orders, lexicographic sums, products, enumeration, algorithmic approaches and the role of algebraic topology. Since there are few prerequisites, the text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory class. After working through a comparatively lean core, the reader can choose from a diverse range of topics such as structure theory, enumeration or algorithmic aspects. Also presented are some key topics less customary to discrete mathematics/graph theory, including a concise introduction to homology for graphs, and the presentation of forward checking as a more efficient alternative to the standard backtracking algorithm. The coverage throughout provides a solid foundation upon which research can be started by a mathematically mature reader. Rich in exercises, illustrations, and open problems, Ordered Sets: An Introduction is an excellent text for undergraduate and graduate students and a good resource for the interested researcher. Readers will discover order theory's role in discrete mathematics as a supplier of ideas as well as an attractive source of applications.
Ordered Sets And Lattices Ordered Sets And Lattices Ii Volume 152
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Author : Simeon I. Ivanov
language : en
Publisher:
Release Date : 1992
Ordered Sets And Lattices Ordered Sets And Lattices Ii Volume 152 written by Simeon I. Ivanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Lattice theory categories.
This book is another publication in the recent surveys of ordered sets and lattices. The papers, which might be characterized as "reviews of reviews," are based on articles reviewed in the Referativnyibreve Zhurnal: Matematika from 1978 to 1982. For the sake of completeness, the authors also attempted to integrate information from other relevant articles from that period. The bibliography of each paper provides references to the reviews in RZhMat and Mathematical Reviews where one can seek more detailed information. Specifically excluded from consideration in this volume were such topics as al.
Applied Abstract Algebra
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Author : Rudolf Lidl
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Applied Abstract Algebra written by Rudolf Lidl and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
There is at present a growing body of opinion that in the decades ahead discrete mathematics (that is, "noncontinuous mathematics"), and therefore parts of applicable modern algebra, will be of increasing importance. Cer tainly, one reason for this opinion is the rapid development of computer science, and the use of discrete mathematics as one of its major tools. The purpose of this book is to convey to graduate students or to final-year undergraduate students the fact that the abstract algebra encountered pre viously in a first algebra course can be used in many areas of applied mathematics. It is often the case that students who have studied mathematics go into postgraduate work without any knowledge of the applicability of the structures they have studied in an algebra course. In recent years there have emerged courses and texts on discrete mathe matics and applied algebra. The present text is meant to add to what is available, by focusing on three subject areas. The contents of this book can be described as dealing with the following major themes: Applications of Boolean algebras (Chapters 1 and 2). Applications of finite fields (Chapters 3 to 5). Applications of semigroups (Chapters 6 and 7).
Ordered Sets
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Author : Ivan Rival
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Ordered Sets written by Ivan Rival and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Computers categories.
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.
The Theory Of Lattice Ordered Groups
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Author : V.M. Kopytov
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
The Theory Of Lattice Ordered Groups written by V.M. Kopytov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-03-09 with Mathematics categories.
A partially ordered group is an algebraic object having the structure of a group and the structure of a partially ordered set which are connected in some natural way. These connections were established in the period between the end of 19th and beginning of 20th century. It was realized that ordered algebraic systems occur in various branches of mathemat ics bound up with its fundamentals. For example, the classification of infinitesimals resulted in discovery of non-archimedean ordered al gebraic systems, the formalization of the notion of real number led to the definition of ordered groups and ordered fields, the construc tion of non-archimedean geometries brought about the investigation of non-archimedean ordered groups and fields. The theory of partially ordered groups was developed by: R. Dedekind, a. Holder, D. Gilbert, B. Neumann, A. I. Mal'cev, P. Hall, G. Birkhoff. These connections between partial order and group operations allow us to investigate the properties of partially ordered groups. For exam ple, partially ordered groups with interpolation property were intro duced in F. Riesz's fundamental paper [1] as a key to his investigations of partially ordered real vector spaces, and the study of ordered vector spaces with interpolation properties were continued by many functional analysts since. The deepest and most developed part of the theory of partially ordered groups is the theory of lattice-ordered groups. In the 40s, following the publications of the works by G. Birkhoff, H. Nakano and P.
Matroid Applications
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Author : Neil White
language : en
Publisher: Cambridge University Press
Release Date : 1992-03-05
Matroid Applications written by Neil White and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-03-05 with Mathematics categories.
This volume, the third in a sequence that began with The Theory of Matroids and Combinatorial Geometries, concentrates on the applications of matroid theory to a variety of topics from engineering (rigidity and scene analysis), combinatorics (graphs, lattices, codes and designs), topology and operations research (the greedy algorithm).