Author: George Grätzer

Publisher: Springer Science & Business Media

ISBN: 9783034800181

Category: Mathematics

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Search Results for: lattice-theory-foundation

## Lattice Theory: Foundation

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
## Lattice Theory: Special Topics and Applications

George Grätzer's Lattice Theory: Foundation is his third book on lattice theory (General Lattice Theory, 1978, second edition, 1998). In 2009, Grätzer considered updating the second edition to reflect some exciting and deep developments. He soon realized that to lay the foundation, to survey the contemporary field, to pose research problems, would require more than one volume and more than one person. So Lattice Theory: Foundation provided the foundation. Now we complete this project with Lattice Theory: Special Topics and Applications, in two volumes, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This second volume is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
## General Lattice Theory

"Grätzer’s 'General Lattice Theory' has become the lattice theorist’s bible. Now we have the second edition, in which the old testament is augmented by a new testament. The new testament gospel is provided by leading and acknowledged experts in their fields. This is an excellent and engaging second edition that will long remain a standard reference." --MATHEMATICAL REVIEWS
## Lattice Theory

This three-volume-set comprises the complete lattice theory project. Volume 1 of the set, Lattice Theory: Foundation, is the revised and enlarged third edition of General Lattice Theory. It focuses on introducing the field and covers the fundamental concepts and results. The two Special Topics and Applications volumes (volumes 2 and 3 of the set), jointly edited by George Grätzer and Friedrich Wehrung, update the reader on some of the vast areas not in Foundation. Volume 1 is divided into three parts. Part I. Topology and Lattices includes two chapters by Klaus Keimel, Jimmie Lawson and Ales Pultr, Jiri Sichler. Part II. Special Classes of Finite Lattices comprises four chapters by Gabor Czedli, George Grätzer and Joseph P. S. Kung. Part III. Congruence Lattices of Infinite Lattices and Beyond includes four chapters by Friedrich Wehrung and George Grätzer. Volume 2 is divided into ten chapters contributed by K. Adaricheva, N. Caspard, R. Freese, P. Jipsen, J.B. Nation, N. Reading, H. Rose, L. Santocanale, and F. Wehrung.
## The Congruences of a Finite Lattice

This is a self-contained exposition by one of the leading experts in lattice theory, George Grätzer, presenting the major results of the last 70 years on congruence lattices of finite lattices, featuring the author's signature Proof-by-Picture method. Key features: * Insightful discussion of techniques to construct "nice" finite lattices with given congruence lattices and "nice" congruence-preserving extensions * Contains complete proofs, an extensive bibliography and index, and over 140 illustrations * This new edition includes two new parts on Planar Semimodular Lattices and The Order of Principle Congruences, covering the research of the last 10 years The book is appropriate for a one-semester graduate course in lattice theory, and it is a practical reference for researchers studying lattices. Reviews of the first edition: "There exist a lot of interesting results in this area of lattice theory, and some of them are presented in this book. [This] monograph...is an exceptional work in lattice theory, like all the contributions by this author. ... The way this book is written makes it extremely interesting for the specialists in the field but also for the students in lattice theory. Moreover, the author provides a series of companion lectures which help the reader to approach the Proof-by-Picture sections." (Cosmin Pelea, Studia Universitatis Babes-Bolyai Mathematica, Vol. LII (1), 2007) "The book is self-contained, with many detailed proofs presented that can be followed step-by-step. [I]n addition to giving the full formal details of the proofs, the author chooses a somehow more pedagogical way that he calls Proof-by-Picture, somehow related to the combinatorial (as opposed to algebraic) nature of many of the presented results. I believe that this book is a much-needed tool for any mathematician wishing a gentle introduction to the field of congruences representations of finite lattices, with emphasis on the more 'geometric' aspects." —Mathematical Reviews
## Semimodular Lattices

## Multimedia and Internet Systems: Theory and Practice

Aleksander Zgrzywa, Kazimierz Choroś, and Andrzej Siemiński (Eds.) Multimedia and Internet Systems: Theory and Practice During the last 20 years we have witnessed a rapid development of Multimedia and Network Information Systems. What is even more important, the pace of change does not show any sign of slowing. When we look back we see how many research projects that have originated at various universities or in research facilities are now part of our everyday life. This monograph offers the reader a very broad review of the most recent scientific investigations in that area. The book is a collection of carefully selected and the most representative investigations, solutions, and applications presented by scientific teams from several countries. The content of the monograph has been divided into four parts: 1. Multimedia Information Technology 2. Information Systems Specification 3. Information Systems Applications 4. Web Systems and Network Technologies The book is aiming to attract more scholars to work on the area of multimedia and Internet applications and to inspire the research community already working on the domain.
## An Invitation to General Algebra and Universal Constructions

Rich in examples and intuitive discussions, this book presents General Algebra using the unifying viewpoint of categories and functors. Starting with a survey, in non-category-theoretic terms, of many familiar and not-so-familiar constructions in algebra (plus two from topology for perspective), the reader is guided to an understanding and appreciation of the general concepts and tools unifying these constructions. Topics include: set theory, lattices, category theory, the formulation of universal constructions in category-theoretic terms, varieties of algebras, and adjunctions. A large number of exercises, from the routine to the challenging, interspersed through the text, develop the reader's grasp of the material, exhibit applications of the general theory to diverse areas of algebra, and in some cases point to outstanding open questions. Graduate students and researchers wishing to gain fluency in important mathematical constructions will welcome this carefully motivated book.
## Der Rabe

„Ängstlich in das Dunkel starrend blieb ich stehn, verwundert, harrend ...“ „Der Rabe“ brachte Edgar Allan Poe den Durchbruch als Lyriker. Sein bekanntestes Gedicht zählt bis heute zum unvergänglichen Erbe der Dichtkunst. In 108 Versen schildert er den mitternächtlichen Besuch eines Raben bei einem Verzweifelten, dessen Geliebte Lenore starb. Die erste deutsche Übersetzung von Elise von Hohenhausen findet sich hier neu interpretiert und illustriert von Marta Monika Czerwinski. Der Name steht für schaurige und düstere Abgründe: Edgar Allan Poe (1809-1849) gilt als Wegbereiter des Symbolismus und Meister des subtilen Horrors. Poes Gedichte, Erzählungen und Kurzgeschichten zählen zu den großen Werken seiner Zeit.
## Concept Lattices and Their Applications

As the refereed proceedings of the Fourth International Conference on Concept Lattices and their Applications, CLA 2006, these 18 revised full papers, together with 3 invited contributions, presented were carefully reviewed and selected from 41 submissions.
## Introduction to Lattices and Order

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.
## Elementare Zahlentheorie

Landau's monumental treatise is a virtual encyclopedia of number theory and is universally recognized as the standard work on the subject. The text is in German.
## Formal Concept Analysis

This book constitutes the refereed proceedings of the 12th International Conference on Formal Concept Analysis, ICFCA 2014, held in Cluj-Napoca, Romania, in June 2014. The 16 regular papers presented together with 3 invited talks were carefully reviewed and selected from 39 submissions. The papers in this volume cover a rich range of FCA aspects, such as theory, enhanced FCA. Knowledge discovery and knowledge spaces, as well as methods and applications. In addition the book contains a reprint of the first publication "Sub direct decomposition of concept lattices" by Rudolf Wille.
## Between Mind and Computer

The ?Fuzzy Explosion? emanating from Japan has compelled more people than ever to ponder the meaning and potential of fuzzy engineering. Scientists all over are now beginning to harness the power of fuzzy recognition and decision-making ? reminescent of the way the human mind works ? in computer applications.In this book a blue-ribbon list of contributors discusses the latest developments in topics such as possibility logic programming, truth-valued flow inference, fuzzy neural-logic networks and default knowledge representation. This volume is the first in a series aiming to document advances in fuzzy set theory and its applications.
## Komplexitätstheorie und Kryptologie

Während die Kryptologie Konzepte und Methoden aus der Komplexitätstheorie verwendet, ist die Forschung in der Komplexitätstheorie wiederum oft durch Fragen aus der Kryptologie motiviert. Der Band hebt die enge Verflechtung dieser beiden Gebiete hervor und führt auf verständlicher Weise in das faszinierende Gebiet der „Kryptokomplexität" ein. Das Buch enthält zahlreiche Abbildungen und Übungsaufgaben sowie ein ausführliches Stichwort- und Literaturverzeichnis. Es eignet sich für Studierende der Informatik, Mathematik oder Ingenieurswissenschaften.
## Vorlesungen über zahlentheorie,

## Positive Operators and Semigroups on Banach Lattices

Proceedings of a Caribbean Mathematics Foundation Conference 1990
## Computeralgebra

Das Lehrbuch führt in das Gebiet der Computeralgebra ein. Neben dem Standardkanon behandelt es Themen für weiterführende Vorlesungen, die bislang nicht in Lehrbuchform erschienen sind. Durch den Einsatz realer Implementierungen anstelle von Pseudocode sind die Algorithmen sofort anwendbar und überprüfbar. Verwendbar mit Mathematica, Maple oder MuPAD. Durch den ausführlichen Index empfiehlt sich der Band auch als Nachschlagewerk.
## Graduate Studies

## Philosophie der Mathematik und Naturwissenschaft

Hermann Weyls "Philosophie der Mathematik und Naturwissenschaft" erschien erstmals 1928 als Beitrag zu dem von A. Bäumler und M. Schröter herausgegebenen "Handbuch der Philosophie". Die amerikanische Ausgabe, auf der die deutsche Übersetzung von Gottlob Kirschmer beruht, erschien 1949 bei Princeton University Press. Das nunmehr bereits in der 8. Auflage vorliegende Werk ist längst auch in Deutschland zum Standardwerk geworden.

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Author: George Grätzer

Publisher: Springer Science & Business Media

ISBN: 9783034800181

Category: Mathematics

Page: 614

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Author: George Grätzer,Friedrich Wehrung

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ISBN: 3319442368

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*Second edition*

Author: George Grätzer

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ISBN: 9783764369965

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*Set*

Author: George Grätzer,Friedrich Wehrung

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*A "Proof-by-Picture" Approach*

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Author: George M. Bergman

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*Mit Illustrationen von Marta Monika Czerwinski*

Author: Edgar Allan Poe

Publisher: SEVERUS Verlag

ISBN: 3863478258

Category: Fiction

Page: 88

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*Fourth International Conference, CLA 2006 Tunis, Tunisia, October 30-November 1, 2006 Selected Papers*

Author: Sadok Ben Yahia,Engelbert Mephu Nguifo

Publisher: Springer Science & Business Media

ISBN: 3540789200

Category: Computers

Page: 283

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Author: B. A. Davey,H. A. Priestley

Publisher: Cambridge University Press

ISBN: 9780521784511

Category: Mathematics

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Author: Edmund Landau

Publisher: American Mathematical Soc.

ISBN: 0821836528

Category: Mathematics

Page: 180

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*12th International Conference, ICFCA 2014, Cluj-Napoca, Romania , June 10-13, 2014. Proceedings*

Author: Cynthia Vera Glodeanu,Mehdi Kaytoue,Christian Sacarea

Publisher: Springer

ISBN: 331907248X

Category: Computers

Page: 297

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*Fuzzy Science and Engineering*

Author: P.-Z. Wang,K.F. Loe

Publisher: World Scientific

ISBN: 9789810236632

Category: Mathematics

Page: 387

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*Eine Einführung in Kryptokomplexität*

Author: Jörg Rothe

Publisher: Springer-Verlag

ISBN: 3540797459

Category: Computers

Page: 535

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Author: Peter Gustav Lejeune Dirichlet

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Category: Number theory

Page: 414

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Author: Caribbean Mathematics Foundation

Publisher: Springer Science & Business Media

ISBN: 9780792319641

Category: Mathematics

Page: 152

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*Eine algorithmisch orientierte Einführung*

Author: Wolfram Koepf

Publisher: Springer-Verlag

ISBN: 3540298959

Category: Mathematics

Page: 515

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*Nach der 2. Auflage des amerikanischen Werkes übersetzt und bearbeitet von Gottlob Kirschmer*

Author: Herrmann Weyl

Publisher: Walter de Gruyter GmbH & Co KG

ISBN: 3486849905

Category: Mathematics

Page: 406

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