The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of Lattices
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The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of Lattices
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Soc.
Release Date : 1977
The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of 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 1977 with Mathematics categories.
A variety (equational class) of lattices is said to be finitely based if there exists a finite set of identities defining the variety. Let [capital script]M [infinity symbol] [over][subscript italic]n denote the lattice variety generated by all modular lattices of width not exceeding [subscript italic]n. [capital script]M [infinity symbol] [over]1 and [capital script]M [infinity symbol] [over]2 are both the class of all distributive lattices and consequently finitely based. B. Jónsson has shown that [capital script]M [infinity symbol] [over]3 is also finitely based. On the other hand, K. Baker has shown that [capital script]M [infinity symbol] [over][subscript italic]n is not finitely based for 5 [less than or equal to symbol] [italic]n [less than] [lowercase Greek]Omega. This paper settles the finite bases problem for [capital script]M [infinity symbol] [over]4.
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.
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.
The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of Lattices
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Author : Ralph S. Freese
language : en
Publisher:
Release Date : 1977
The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of Lattices written by Ralph S. Freese and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1977 with Lattice theory categories.
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.
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
General Lattice Theory
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Author : G. Grätzer
language : en
Publisher: Birkhäuser
Release Date : 2012-12-06
General Lattice Theory written by G. Grätzer and has been published by Birkhäuser this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Social Science categories.
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]).
Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev
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Author : Leonid A. Bokut'
language : en
Publisher: American Mathematical Soc.
Release Date : 1992
Proceedings Of The International Conference On Algebra Dedicated To The Memory Of A I Mal Cev written by Leonid A. Bokut' 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 1992 with Algebra categories.
The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of Lattices
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Author : Ralph S. Freese
language : en
Publisher: American Mathematical Soc.
Release Date : 1977-12-31
The Structure Of Modular Lattices Of Width Four With Applications To Varieties Of 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 1977-12-31 with Mathematics categories.
Houston Journal Of Mathematics
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Author :
language : en
Publisher:
Release Date : 1979
Houston Journal Of Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979 with Mathematics categories.