Ordered Sets And Lattices Ii

Author : Anonim
Publisher : American Mathematical Soc.
Page : 262 pages
File Size : 43,6 Mb
Release : 2024-06-11
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 : Steven Roman
Publisher : Springer Science & Business Media
Page : 307 pages
File Size : 41,6 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 : 42,6 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 : Bernd Schröder
Publisher : Springer Science & Business Media
Page : 401 pages
File Size : 55,5 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 : B. A. Davey,H. A. Priestley
Publisher : Cambridge University Press
Page : 309 pages
File Size : 48,7 Mb
Release : 2002-04-18
Category : Mathematics
ISBN : 9781107717527

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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 : B. A. Davey,Hilary A. Priestley
Publisher : Unknown
Page : 248 pages
File Size : 45,7 Mb
Release : 1990
Category : Lattice theory
ISBN : 0521367662

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

This is the first introductory textbook on ordered sets and lattices, and covers both the basic theory and its applications. The importance of ordered structures has been increasingly recognised in recent years due to an explosion of interest in computer science and all areas of discrete mathematics. The authors provide a thorough introduction to ordered sets, lattices, distributive lattices and Boolean algebras. Ordered sets, and in particular lattices, can be represented pictorially, and this key feature is emphasised throughout. Lattices are also considered as algebraic structures and their study from this viewpoint reinforces ideas encountered in the theory of groups and rings. The representation of distributive lattices by ordered topological spaces is presented; a self-contained treatment of the requisite topology is included. Two chapters are devoted to topics with application to computer science. These cover complete partial orders, domains (including their relation to information systems), and fixpoint theory. Another chapter deals with formal concept analysis - a new and important application of lattice theory of interest to mathematicians and social scientists. Prerequisites are minimal; all that is assumed is exposure to the notation of set theory and elementary abstract algebra. The numerous classroom-tested exercises will make the book especially useful for course accompaniment, but it will also be valuable as a background reference for mathematicians, logicians and computer scientists.

Author : Bernd Siegfried Walter Schröder
Publisher : Springer Science & Business Media
Page : 420 pages
File Size : 53,7 Mb
Release : 2003
Category : Mathematics
ISBN : 0817641289

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Ordered Sets by Bernd Siegfried Walter Schröder Pdf

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.

Author : Anonim
Publisher : Unknown
Page : 128 pages
File Size : 46,8 Mb
Release : 1955
Category : Group theory
ISBN : 0821831216

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American Mathematical Society Translations by Anonim Pdf

Author : Bernd Schröder
Publisher : Birkhäuser
Page : 420 pages
File Size : 51,5 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 : Egbert Harzheim
Publisher : Springer Science & Business Media
Page : 391 pages
File Size : 47,9 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 : Nathalie Caspard,Bruno Leclerc,Bernard Monjardet
Publisher : Cambridge University Press
Page : 351 pages
File Size : 50,6 Mb
Release : 2012-01-26
Category : Mathematics
ISBN : 9781107013698

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

A comprehensive account that gives equal attention to the combinatorial, logical and applied aspects of partially ordered sets.

Author : M.E Anderson,T.H. Feil
Publisher : Springer Science & Business Media
Page : 197 pages
File Size : 48,9 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 : Rudolf Lidl,Günter Pilz
Publisher : Springer Science & Business Media
Page : 561 pages
File Size : 47,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461564652

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Applied Abstract Algebra by Rudolf Lidl,Günter Pilz Pdf

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).

Author : American Mathematical Society
Publisher : Unknown
Page : 128 pages
File Size : 41,7 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 : Neil White
Publisher : Cambridge University Press
Page : 377 pages
File Size : 50,8 Mb
Release : 1992-03-05
Category : Mathematics
ISBN : 9780521381659

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Matroid Applications by Neil White Pdf

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).