The Congruences Of A Finite Lattice PDF Download
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| Author | : George Grätzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 287 |
| Release | : 2007-05-24 |
| Genre | : Mathematics |
| ISBN | : 0817644628 |
Download The Congruences of a Finite Lattice Book in PDF, ePub and Kindle
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
| Author | : George Gr Tzer |
| Publisher | : |
| Total Pages | : 308 |
| Release | : 2011-03-21 |
| Genre | : |
| ISBN | : 9780817670344 |
Download The Congruences of a Finite Lattice Book in PDF, ePub and Kindle
| Author | : George Grätzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 639 |
| Release | : 2011-02-14 |
| Genre | : Mathematics |
| ISBN | : 3034800185 |
Download Lattice Theory: Foundation Book in PDF, ePub and Kindle
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
| Author | : G. Grätzer |
| Publisher | : Birkhäuser |
| Total Pages | : 392 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3034876335 |
Download General Lattice Theory Book in PDF, ePub and Kindle
In the first half of the nineteenth century, George Boole's attempt to formalize propositional logic led to the concept of Boolean algebras. While investigating the axiomatics of Boolean algebras at the end of the nineteenth century, Charles S. Peirce and Ernst Schröder found it useful to introduce the lattice concept. Independently, Richard Dedekind's research on ideals of algebraic numbers led to the same discov ery. In fact, Dedekind also introduced modularity, a weakened form of distri butivity. Although some of the early results of these mathematicians and of Edward V. Huntington are very elegant and far from trivial, they did not attract the attention of the mathematical community. It was Garrett Birkhoff's work in the mid-thirties that started the general develop ment of lattice theory. In a brilliant series of papers he demonstrated the importance of lattice theory and showed that it provides a unifying framework for hitherto unrelated developments in many mathematical disciplines. Birkhoff himself, Valere Glivenko, Karl Menger, John von Neumann, Oystein Ore, and others had developed enough of this new field for Birkhoff to attempt to "seIl" it to the general mathematical community, which he did with astonishing success in the first edition of his Lattice Theory. The further development of the subject matter can best be followed by com paring the first, second, and third editions of his book (G. Birkhoff [1940], [1948], and [1967]).
| Author | : Keith Kearnes |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 183 |
| Release | : 2013-02-26 |
| Genre | : Mathematics |
| ISBN | : 0821883232 |
Download The Shape of Congruence Lattices Book in PDF, ePub and Kindle
This monograph is concerned with the relationships between Maltsev conditions, commutator theories and the shapes of congruence lattices in varieties of algebras. The authors develop the theories of the strong commutator, the rectangular commutator, the strong rectangular commutator, as well as a solvability theory for the nonmodular TC commutator. They prove that a residually small variety that satisfies a congruence identity is congruence modular.
| Author | : George Grätzer |
| Publisher | : Springer |
| Total Pages | : 472 |
| Release | : 2014-08-27 |
| Genre | : Mathematics |
| ISBN | : 3319064134 |
Download Lattice Theory: Special Topics and Applications Book in PDF, ePub and Kindle
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.
| Author | : David Charles Hobby |
| Publisher | : |
| Total Pages | : 220 |
| Release | : 1988 |
| Genre | : Mathematics |
| ISBN | : |
Download The Structure of Finite Algebras Book in PDF, ePub and Kindle
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.
| Author | : Peter Jipsen |
| Publisher | : Springer |
| Total Pages | : 171 |
| Release | : 2006-11-15 |
| Genre | : Mathematics |
| ISBN | : 3540475141 |
Download Varieties of Lattices Book in PDF, ePub and Kindle
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.
| Author | : B. A. Davey |
| Publisher | : Cambridge University Press |
| Total Pages | : 316 |
| Release | : 2002-04-18 |
| Genre | : Mathematics |
| ISBN | : 1107717523 |
Download Introduction to Lattices and Order Book in PDF, ePub and Kindle
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 | : George Grätzer |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 601 |
| Release | : 2008-12-15 |
| Genre | : Mathematics |
| ISBN | : 0387774874 |
Download Universal Algebra Book in PDF, ePub and Kindle
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.
