Universal Algebra And Lattice Theory
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Universal Algebra And Lattice Theory
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Author : R.S. Freese
language : en
Publisher: Springer
Release Date : 2006-11-15
Universal Algebra And Lattice Theory written by R.S. Freese 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.
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.
Universal Algebra And Lattice Theory
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Author : Stephen D. Comer
language : en
Publisher:
Release Date : 2014-09-01
Universal Algebra And Lattice Theory written by Stephen D. Comer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-09-01 with categories.
Lattices Semigroups And Universal Algebra
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Author : Jorge Almeida
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-11-11
Lattices Semigroups And Universal Algebra written by Jorge Almeida 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 2013-11-11 with Mathematics categories.
This volume contains papers which, for the most part, are based on talks given at an international conference on Lattices, Semigroups, and Universal Algebra that was held in Lisbon, Portugal during the week of June 20-24, 1988. The conference was dedicated to the memory of Professor Antonio Almeida Costa, a Portuguese mathematician who greatly contributed to the development of th algebra in Portugal, on the 10 anniversary of his death. The themes of the conference reflect some of his research interests and those of his students. The purpose of the conference was to gather leading experts in Lattices, Semigroups, and Universal Algebra and to promote a discussion of recent developments and trends in these areas. All three fields have grown rapidly during the last few decades with varying degrees of interaction. Lattice theory and Universal Algebra have historically evolved alongside with a large overlap between the groups of researchers in the two fields. More recently, techniques and ideas of these theories have been used extensively in the theory of semigroups. Conversely, some developments in that area may inspire further developments in Universal Algebra. On the other hand, techniques of semi group theory have naturally been employed in the study of semilattices. Several papers in this volume elaborate on these interactions.
Universal Algebra And Lattice Theory Proceedings Of The International Conference 1984
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Author :
language : en
Publisher:
Release Date : 1984
Universal Algebra And Lattice Theory Proceedings Of The International Conference 1984 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1984 with categories.
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 And Orders
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Author : Ivo G. Rosenberg
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09
Algebras And Orders written by Ivo G. Rosenberg 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 2013-03-09 with Mathematics categories.
In the summer of 1991 the Department of Mathematics and Statistics of the Universite de Montreal was fortunate to host the NATO Advanced Study Institute "Algebras and Orders" as its 30th Seminaire de mathematiques superieures (SMS), a summer school with a long tradition and well-established reputation. This book contains the contributions of the invited speakers. Universal algebra- which established itself only in the 1930's- grew from traditional algebra (e.g., groups, modules, rings and lattices) and logic (e.g., propositional calculus, model theory and the theory of relations). It started by extending results from these fields but by now it is a well-established and dynamic discipline in its own right. One of the objectives of the ASI was to cover a broad spectrum of topics in this field, and to put in evidence the natural links to, and interactions with, boolean algebra, lattice theory, topology, graphs, relations, automata, theoretical computer science and (partial) orders. The theory of orders is a relatively young and vigorous discipline sharing certain topics as well as many researchers and meetings with universal algebra and lattice theory. W. Taylor surveyed the abstract clone theory which formalizes the process of compos ing operations (i.e., the formation of term operations) of an algebra as a special category with countably many objects, and leading naturally to the interpretation and equivalence of varieties.
Universal Algebra And Lattice Theory Proceedings Of The International Conference 4
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Author :
language : en
Publisher:
Release Date : 1983
Universal Algebra And Lattice Theory Proceedings Of The International Conference 4 written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983 with categories.
Algebras Lattices Varieties
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Author : Ralph N. McKenzie
language : en
Publisher: American Mathematical Society
Release Date : 2018-07-09
Algebras Lattices Varieties written by Ralph N. McKenzie 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 2018-07-09 with Mathematics categories.
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.
Residuated Lattices An Algebraic Glimpse At Substructural Logics
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Author : Nikolaos Galatos
language : en
Publisher: Elsevier
Release Date : 2007-04-25
Residuated Lattices An Algebraic Glimpse At Substructural Logics written by Nikolaos Galatos and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-04-25 with Mathematics categories.
The book is meant to serve two purposes. The first and more obvious one is to present state of the art results in algebraic research into residuated structures related to substructural logics. The second, less obvious but equally important, is to provide a reasonably gentle introduction to algebraic logic. At the beginning, the second objective is predominant. Thus, in the first few chapters the reader will find a primer of universal algebra for logicians, a crash course in nonclassical logics for algebraists, an introduction to residuated structures, an outline of Gentzen-style calculi as well as some titbits of proof theory - the celebrated Hauptsatz, or cut elimination theorem, among them. These lead naturally to a discussion of interconnections between logic and algebra, where we try to demonstrate how they form two sides of the same coin. We envisage that the initial chapters could be used as a textbook for a graduate course, perhaps entitled Algebra and Substructural Logics. As the book progresses the first objective gains predominance over the second. Although the precise point of equilibrium would be difficult to specify, it is safe to say that we enter the technical part with the discussion of various completions of residuated structures. These include Dedekind-McNeille completions and canonical extensions. Completions are used later in investigating several finiteness properties such as the finite model property, generation of varieties by their finite members, and finite embeddability. The algebraic analysis of cut elimination that follows, also takes recourse to completions. Decidability of logics, equational and quasi-equational theories comes next, where we show how proof theoretical methods like cut elimination are preferable for small logics/theories, but semantic tools like Rabin's theorem work better for big ones. Then we turn to Glivenko's theorem, which says that a formula is an intuitionistic tautology if and only if its double negation is a classical one. We generalise it to the substructural setting, identifying for each substructural logic its Glivenko equivalence class with smallest and largest element. This is also where we begin investigating lattices of logics and varieties, rather than particular examples. We continue in this vein by presenting a number of results concerning minimal varieties/maximal logics. A typical theorem there says that for some given well-known variety its subvariety lattice has precisely such-and-such number of minimal members (where values for such-and-such include, but are not limited to, continuum, countably many and two). In the last two chapters we focus on the lattice of varieties corresponding to logics without contraction. In one we prove a negative result: that there are no nontrivial splittings in that variety. In the other, we prove a positive one: that semisimple varieties coincide with discriminator ones. Within the second, more technical part of the book another transition process may be traced. Namely, we begin with logically inclined technicalities and end with algebraically inclined ones. Here, perhaps, algebraic rendering of Glivenko theorems marks the equilibrium point, at least in the sense that finiteness properties, decidability and Glivenko theorems are of clear interest to logicians, whereas semisimplicity and discriminator varieties are universal algebra par exellence. It is for the reader to judge whether we succeeded in weaving these threads into a seamless fabric.