The Shape of Congruence Lattices

The Shape of Congruence Lattices
Title The Shape of Congruence Lattices PDF eBook
Author Keith Kearnes
Publisher American Mathematical Soc.
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.

Algebras and Lattices in Hawai'i: honoring Ralph Freese, Bill Lampe, and JB Nation

Algebras and Lattices in Hawai'i: honoring Ralph Freese, Bill Lampe, and JB Nation
Title Algebras and Lattices in Hawai'i: honoring Ralph Freese, Bill Lampe, and JB Nation PDF eBook
Author Kira Adaricheva
Publisher Lulu.com
Pages 119
Release 2018-04-26
Genre Science
ISBN 1387772481

Download Algebras and Lattices in Hawai'i: honoring Ralph Freese, Bill Lampe, and JB Nation Book in PDF, Epub and Kindle

Conference proceedings for Algebras and Lattices in Hawaii, honoring Ralph Freese, William Lampe, and JB Nation.

Universal Algebra and Lattice Theory

Universal Algebra and Lattice Theory
Title Universal Algebra and Lattice Theory PDF eBook
Author R.S. Freese
Publisher Springer
Pages 314
Release 2006-11-15
Genre Mathematics
ISBN 3540409548

Download Universal Algebra and Lattice Theory Book in PDF, Epub and Kindle

Lattice Theory: Special Topics and Applications

Lattice Theory: Special Topics and Applications
Title Lattice Theory: Special Topics and Applications PDF eBook
Author George Grätzer
Publisher Birkhäuser
Pages 625
Release 2016-10-08
Genre Mathematics
ISBN 3319442368

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, 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.

Algebras, Lattices, Varieties

Algebras, Lattices, Varieties
Title Algebras, Lattices, Varieties PDF eBook
Author Ralph N. McKenzie
Publisher American Mathematical Society
Pages 386
Release 2018-07-09
Genre Mathematics
ISBN 1470442957

Download Algebras, Lattices, Varieties Book in PDF, Epub and Kindle

This book presents the foundations of a general theory of algebras. Often called “universal algebra”, this theory provides a common framework for all algebraic systems, including groups, rings, modules, fields, and lattices. Each chapter is replete with useful illustrations and exercises that solidify the reader's understanding. The book begins by developing the main concepts and working tools of algebras and lattices, and continues with examples of classical algebraic systems like groups, semigroups, monoids, and categories. The essence of the book lies in Chapter 4, which provides not only basic concepts and results of general algebra, but also the perspectives and intuitions shared by practitioners of the field. The book finishes with a study of possible uniqueness of factorizations of an algebra into a direct product of directly indecomposable algebras. There is enough material in this text for a two semester course sequence, but a one semester course could also focus primarily on Chapter 4, with additional topics selected from throughout the text.

The Lattice of Subquasivarieties of a Locally Finite Quasivariety

The Lattice of Subquasivarieties of a Locally Finite Quasivariety
Title The Lattice of Subquasivarieties of a Locally Finite Quasivariety PDF eBook
Author Jennifer Hyndman
Publisher Springer
Pages 173
Release 2018-08-28
Genre Computers
ISBN 3319782355

Download The Lattice of Subquasivarieties of a Locally Finite Quasivariety Book in PDF, Epub and Kindle

This book discusses the ways in which the algebras in a locally finite quasivariety determine its lattice of subquasivarieties. The book starts with a clear and comprehensive presentation of the basic structure theory of quasivariety lattices, and then develops new methods and algorithms for their analysis. Particular attention is paid to the role of quasicritical algebras. The methods are illustrated by applying them to quasivarieties of abelian groups, modular lattices, unary algebras and pure relational structures. An appendix gives an overview of the theory of quasivarieties. Extensive references to the literature are provided throughout.

Lattice Theory: Foundation

Lattice Theory: Foundation
Title Lattice Theory: Foundation PDF eBook
Author George Grätzer
Publisher Springer Science & Business Media
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