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

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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

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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

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Algebras, Lattices, Varieties

Algebras, Lattices, Varieties
Title Algebras, Lattices, Varieties PDF eBook
Author Ralph S. Freese
Publisher American Mathematical Society
Pages 496
Release 2022-10-28
Genre Mathematics
ISBN 1470467976

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This book is the second of a three-volume set of books on the theory of algebras, a study that provides a consistent framework for understanding algebraic systems, including groups, rings, modules, semigroups and lattices. Volume I, first published in the 1980s, built the foundations of the theory and is considered to be a classic in this field. The long-awaited volumes II and III are now available. Taken together, the three volumes provide a comprehensive picture of the state of art in general algebra today, and serve as a valuable resource for anyone working in the general theory of algebraic systems or in related fields. The two new volumes are arranged around six themes first introduced in Volume I. Volume II covers the Classification of Varieties, Equational Logic, and Rudiments of Model Theory, and Volume III covers Finite Algebras and their Clones, Abstract Clone Theory, and the Commutator. These topics are presented in six chapters with independent expositions, but are linked by themes and motifs that run through all three volumes.

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

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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

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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

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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.