The Congruences Of A Finite Lattice

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The Congruences Of A Finite Lattice

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Author : George Grätzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2005-11-09

The Congruences Of A Finite Lattice written by George Grätzer 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 2005-11-09 with Mathematics categories.

Self-contained exposition presents the major results on congruence lattices of finite lattices Includes the latest findings from a pioneering researcher in the field Features the author's signature "Proof-by-Picture" method and its conversion to transparencies Contains complete proofs, an extensive bibliography and index, and nearly 80 open problems Excellent grad text and reference

The Congruences Of A Finite Lattice

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Author : George Gr Tzer
language : en
Publisher:
Release Date : 2011-03-21

The Congruences Of A Finite Lattice written by George Gr Tzer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-03-21 with categories.

Lattice Theory Special Topics And Applications

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Author : George Grätzer
language : en
Publisher: Springer
Release Date : 2014-08-27

Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-08-27 with Mathematics categories.

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, written by a distinguished group of experts, to cover some of the vast areas not in Foundation. This first volume 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.

The Structure Of Finite Algebras

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Author : David Charles Hobby
language : en
Publisher:
Release Date : 1988

The Structure Of Finite Algebras written by David Charles Hobby and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988 with Mathematics categories.

The utility of congruence lattices in revealing the structure of general algebras has been recognized since Garrett Birkhoff's pioneering work in the 1930s and 1940s. However, the results presented in this book are of very recent origin: most of them were developed in 1983. The main discovery presented here is that the lattice of congruences of a finite algebra is deeply connected to the structure of that algebra. The theory reveals a sharp division of locally finite varieties of algebras into six interesting new families, each of which is characterized by the behavior of congruences in the algebras. The authors use the theory to derive many new results that will be of interest not only to universal algebraists, but to other algebraists as well. The authors begin with a straightforward and complete development of basic tame congruence theory, a topic that offers great promise for a wide variety of investigations. They then move beyond the consideration of individual algebras to a study of locally finite varieties. A list of open problems closes the work.

Introduction To Lattice Theory With Computer Science Applications

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Author : Vijay K. Garg
language : en
Publisher: John Wiley & Sons
Release Date : 2016-03-02

Introduction To Lattice Theory With Computer Science Applications written by Vijay K. Garg and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-03-02 with Computers categories.

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.

Varieties Of Lattices

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Author : Peter Jipsen
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1992-12-14

Varieties Of Lattices written by Peter Jipsen and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992-12-14 with Mathematics categories.

The study of lattice varieties is a field that has experienced rapid growth in the last 30 years, but many of the interesting and deep results discovered in that period have so far only appeared in research papers. The aim of this monograph is to present the main results about modular and nonmodular varieties, equational bases and the amalgamation property in a uniform way. The first chapter covers preliminaries that make the material accessible to anyone who has had an introductory course in universal algebra. Each subsequent chapter begins with a short historical introduction which sites the original references and then presents the results with complete proofs (in nearly all cases). Numerous diagrams illustrate the beauty of lattice theory and aid in the visualization of many proofs. An extensive index and bibliography also make the monograph a useful reference work.

Set Theory

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Author : Daniel W. Cunningham
language : en
Publisher: Cambridge University Press
Release Date : 2016-07-18

Set Theory written by Daniel W. Cunningham 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 2016-07-18 with Mathematics categories.

Set theory can be considered a unifying theory for mathematics. This book covers the fundamentals of the subject.

Universal Algebra

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Author : George Grätzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2008-12-15

Universal Algebra written by George Grätzer 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.

Universal Algebra has become the most authoritative, consistently relied on text in a field with applications in other branches of algebra and other fields such as combinatorics, geometry, and computer science. Each chapter is followed by an extensive list of exercises and problems. The "state of the art" account also includes new appendices (with contributions from B. Jónsson, R. Quackenbush, W. Taylor, and G. Wenzel) and a well selected additional bibliography of over 1250 papers and books which makes this an indispensable new edition for students, faculty, and workers in the field.

Function Algebras On Finite Sets

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Author : Dietlinde Lau
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-11-23

Function Algebras On Finite Sets written by Dietlinde Lau 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 2006-11-23 with Mathematics categories.

Functions which are defined on finite sets occur in almost all fields of mathematics. For more than 80 years algebras whose universes are such functions (so-called function algebras), have been intensively studied. This book gives a broad introduction to the theory of function algebras and leads to the cutting edge of research. To familiarize the reader from the very beginning on with the algebraic side of function algebras the more general concepts of the Universal Algebra is given in the first part of the book. The second part on fuction algebras covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, clone theory. This book is an insdispensible source on function algebras for graduate students and researchers in mathematical logic and theoretical computer science.

General Lattice Theory

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Author : George Grätzer
language : en
Publisher: Springer Science & Business Media
Release Date : 2002-11-21

General Lattice Theory written by George Grätzer 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 2002-11-21 with Mathematics categories.

"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