Nonmodular Lattice Varieties
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Nonmodular Lattice Varieties
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Author : Henry Rose
language : en
Publisher: American Mathematical Soc.
Release Date : 1984
Nonmodular Lattice Varieties written by Henry Rose and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with Mathematics categories.
It is shown that there are eight infinite sequences of join irreducible lattice varieties with the following properties: each term of every sequence has the next term as its unique join irreducible cover. The description of these sequences is based on a detailed study of subdirectly irreducible lattices with the unique critical quotients.
Varieties Of Lattices
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Author : Peter Jipsen
language : en
Publisher: Springer
Release Date : 2006-11-15
Varieties Of Lattices written by Peter Jipsen and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 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.
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.
Algebras Lattices Varieties
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Society
Release Date : 2022-10-28
Algebras Lattices Varieties written by Ralph S. Freese and has been published by American Mathematical Society this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-10-28 with Mathematics categories.
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.
Semimodular Lattices
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Author : Manfred Stern
language : en
Publisher: Cambridge University Press
Release Date : 1999-05-13
Semimodular Lattices written by Manfred Stern 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 1999-05-13 with Mathematics categories.
A survey of semimodularity that presents theory and applications in discrete mathematics, group theory and universal algebra.
Axioms For Lattices And Boolean Algebras
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Author : R Padmanabhan
language : en
Publisher: World Scientific
Release Date : 2008-08-11
Axioms For Lattices And Boolean Algebras written by R Padmanabhan and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-08-11 with Mathematics categories.
The importance of equational axioms emerged initially with the axiomatic approach to Boolean algebras, groups, and rings, and later in lattices. This unique research monograph systematically presents minimal equational axiom-systems for various lattice-related algebras, regardless of whether they are given in terms of “join and meet” or other types of operations such as ternary operations. Each of the axiom-systems is coded in a handy way so that it is easy to follow the natural connection among the various axioms and to understand how to combine them to form new axiom systems.A new topic in this book is the characterization of Boolean algebras within the class of all uniquely complemented lattices. Here, the celebrated problem of E V Huntington is addressed, which — according to G Gratzer, a leading expert in modern lattice theory — is one of the two problems that shaped a century of research in lattice theory. Among other things, it is shown that there are infinitely many non-modular lattice identities that force a uniquely complemented lattice to be Boolean, thus providing several new axiom systems for Boolean algebras within the class of all uniquely complemented lattices. Finally, a few related lines of research are sketched, in the form of appendices, including one by Dr Willian McCune of the University of New Mexico, on applications of modern theorem-proving to the equational theory of lattices.
Lattice Theory Special Topics And Applications
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Author : George Grätzer
language : en
Publisher: Birkhäuser
Release Date : 2016-10-08
Lattice Theory Special Topics And Applications written by George Grätzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-10-08 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, 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.
Free Lattices
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Soc.
Release Date : 1995
Free Lattices written by Ralph S. Freese and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1995 with Mathematics categories.
A thorough treatment of free lattices, including such aspects as Whitman's solution to the word problem, bounded monomorphisms and related concepts, totally atomic elements, infinite intervals, computation, term rewrite systems, and varieties. Includes several results that are new or have not been previously published. Annotation copyright by Book News, Inc., Portland, OR
Universal Algebra And Lattice Theory
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Author : Stephen D. Comer
language : en
Publisher: Springer
Release Date : 2006-12-08
Universal Algebra And Lattice Theory written by Stephen D. Comer and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-12-08 with Mathematics categories.
The Shape Of Congruence Lattices
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Author : Keith Kearnes
language : en
Publisher: American Mathematical Soc.
Release Date : 2013-02-26
The Shape Of Congruence Lattices written by Keith Kearnes and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-02-26 with Mathematics categories.
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.