Lattices And Ordered Sets

Author : Steven Roman
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 54,9 Mb
Release : 2008-12-15
Category : Mathematics
ISBN : 9780387789019

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Lattices and Ordered Sets by Steven Roman Pdf

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.

Author : Karl Heinrich Hofmann,Klaus Keimel
Publisher : American Mathematical Soc.
Page : 129 pages
File Size : 54,9 Mb
Release : 1972
Category : Categories (Mathematics).
ISBN : 9780821818220

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A General Character Theory for Partially Ordered Sets and Lattices by Karl Heinrich Hofmann,Klaus Keimel Pdf

Author : B. A. Davey,H. A. Priestley
Publisher : Cambridge University Press
Page : 316 pages
File Size : 48,9 Mb
Release : 2002-04-18
Category : Mathematics
ISBN : 0521784514

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Introduction to Lattices and Order by B. A. Davey,H. A. Priestley Pdf

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.

Author : Anonim
Publisher : American Mathematical Soc.
Page : 262 pages
File Size : 53,9 Mb
Release : 2024-06-30
Category : Mathematics
ISBN : 0821895885

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Ordered Sets and Lattices II by Anonim Pdf

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.

Author : T.S. Blyth
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 52,8 Mb
Release : 2005-04-18
Category : Mathematics
ISBN : 9781852339050

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Lattices and Ordered Algebraic Structures by T.S. Blyth Pdf

"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

Author : Bernd Schröder
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 45,6 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461200536

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Ordered Sets by Bernd Schröder Pdf

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. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Author : Egbert Harzheim
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 51,9 Mb
Release : 2005-02-17
Category : Mathematics
ISBN : 9780387242194

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Ordered Sets by Egbert Harzheim Pdf

The textbook literature on ordered sets is still rather limited. A lot of material is presented in this book that appears now for the first time in a textbook. Order theory works with combinatorial and set-theoretical methods, depending on whether the sets under consideration are finite or infinite. In this book the set-theoretical parts prevail. The book treats in detail lexicographic products and their connections with universally ordered sets, and further it gives thorough investigations on the structure of power sets. Other topics dealt with include dimension theory of ordered sets, well-quasi-ordered sets, trees, combinatorial set theory for ordered sets, comparison of order types, and comparibility graphs. Audience This book is intended for mathematics students and for mathemeticians who are interested in set theory. Only some fundamental parts of naïve set theory are presupposed. Since all proofs are worked out in great detail, the book should be suitable as a text for a course on order theory.

Author : American Mathematical Society
Publisher : Unknown
Page : 128 pages
File Size : 50,7 Mb
Release : 1949
Category : Lattice theory
ISBN : 0821831216

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American Mathematical Society Translations by American Mathematical Society Pdf

Translations of articles on mathematics appearing in various Russian mathematical serials.

Author : M.E Anderson,T.H. Feil
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 49,6 Mb
Release : 2012-12-06
Category : Computers
ISBN : 9789400928718

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Lattice-Ordered Groups by M.E Anderson,T.H. Feil Pdf

The study of groups equipped with a compatible lattice order ("lattice-ordered groups" or "I!-groups") has arisen in a number of different contexts. Examples of this include the study of ideals and divisibility, dating back to the work of Dedekind and continued by Krull; the pioneering work of Hahn on totally ordered abelian groups; and the work of Kantorovich and other analysts on partially ordered function spaces. After the Second World War, the theory of lattice-ordered groups became a subject of study in its own right, following the publication of fundamental papers by Birkhoff, Nakano and Lorenzen. The theory blossomed under the leadership of Paul Conrad, whose important papers in the 1960s provided the tools for describing the structure for many classes of I!-groups in terms of their convex I!-subgroups. A particularly significant success of this approach was the generalization of Hahn's embedding theorem to the case of abelian lattice-ordered groups, work done with his students John Harvey and Charles Holland. The results of this period are summarized in Conrad's "blue notes" [C].

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 54,6 Mb
Release : 1955
Category : Group theory
ISBN : 0821831216

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American Mathematical Society Translations by Anonim Pdf

Author : Nathalie Caspard,Bruno Leclerc,Bernard Monjardet
Publisher : Cambridge University Press
Page : 351 pages
File Size : 42,7 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781107080003

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Finite Ordered Sets by Nathalie Caspard,Bruno Leclerc,Bernard Monjardet Pdf

Ordered sets are ubiquitous in mathematics and have significant applications in computer science, statistics, biology and the social sciences. As the first book to deal exclusively with finite ordered sets, this book will be welcomed by graduate students and researchers in all of these areas. Beginning with definitions of key concepts and fundamental results (Dilworth's and Sperner's theorem, interval and semiorders, Galois connection, duality with distributive lattices, coding and dimension theory), the authors then present applications of these structures in fields such as preference modelling and aggregation, operational research and management, cluster and concept analysis, and data mining. Exercises are included at the end of each chapter with helpful hints provided for some of the most difficult examples. The authors also point to further topics of ongoing research.

Author : T.S. Blyth
Publisher : Springer Science & Business Media
Page : 311 pages
File Size : 46,8 Mb
Release : 2005-11-24
Category : Mathematics
ISBN : 9781846281273

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Lattices and Ordered Algebraic Structures by T.S. Blyth Pdf

"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

Author : Ivan Rival
Publisher : Springer Science & Business Media
Page : 798 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9789400953154

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Graphs and Order by Ivan Rival Pdf

This volume contains the accounts of the principal survey papers presented at GRAPHS and ORDER, held at Banff, Canada from May 18 to May 31, 1984. This conference was supported by grants from the N.A.T.O. Advanced Study Institute programme, the Natural Sciences and Engineering Research Council of Canada and the University of Calgary. We are grateful for all of this considerable support. Almost fifty years ago the first Symposium on Lattice Theory was held in Charlottesville, U.S.A. On that occasion the principal lectures were delivered by G. Birkhoff, O. Ore and M.H. Stone. In those days the theory of ordered sets was thought to be a vigorous relative of group theory. Some twenty-five years ago the Symposium on Partially Ordered Sets and Lattice Theory was held in Monterey, U.S.A. Among the principal speakers at that meeting were R.P. Dilworth, B. Jonsson, A. Tarski and G. Birkhoff. Lattice theory had turned inward: it was concerned primarily with problems about lattices themselves. As a matter of fact the problems that were then posed have, by now, in many instances, been completely solved.

Author : Bernd Schröder
Publisher : Birkhäuser
Page : 420 pages
File Size : 47,9 Mb
Release : 2016-05-11
Category : Mathematics
ISBN : 9783319297880

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Ordered Sets by Bernd Schröder Pdf

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. The text can be used as a focused follow-up or companion to a first proof (set theory and relations) or graph theory course.

Author : Vijay K. Garg
Publisher : John Wiley & Sons
Page : 272 pages
File Size : 55,9 Mb
Release : 2016-03-02
Category : Computers
ISBN : 9781119069737

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Introduction to Lattice Theory with Computer Science Applications by Vijay K. Garg Pdf

A computational perspective on partial order and lattice theory, focusing on algorithms and their applications This book provides a uniform treatment of the theory and applications of lattice theory. The applications covered include tracking dependency in distributed systems, combinatorics, detecting global predicates in distributed systems, set families, and integer partitions. The book presents algorithmic proofs of theorems whenever possible. These proofs are written in the calculational style advocated by Dijkstra, with arguments explicitly spelled out step by step. The author’s intent is for readers to learn not only the proofs, but the heuristics that guide said proofs. Introduction to Lattice Theory with Computer Science Applications: Examines; posets, Dilworth’s theorem, merging algorithms, lattices, lattice completion, morphisms, modular and distributive lattices, slicing, interval orders, tractable posets, lattice enumeration algorithms, and dimension theory Provides end of chapter exercises to help readers retain newfound knowledge on each subject Includes supplementary material at www.ece.utexas.edu/~garg Introduction to Lattice Theory with Computer Science Applications is written for students of computer science, as well as practicing mathematicians.