Function Algebras On Finite Sets

Author : Dietlinde Lau
Publisher : Springer Science & Business Media
Page : 668 pages
File Size : 44,6 Mb
Release : 2006-11-23
Category : Mathematics
ISBN : 9783540360230

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Function Algebras on Finite Sets by Dietlinde Lau Pdf

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Author : Dietlinde Lau
Publisher : Springer
Page : 0 pages
File Size : 53,7 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 3540360220

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Function Algebras on Finite Sets by Dietlinde Lau Pdf

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Author : Dietlinde Lau
Publisher : Springer
Page : 670 pages
File Size : 46,5 Mb
Release : 2006-08-03
Category : Mathematics
ISBN : 3540360220

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Function Algebras on Finite Sets by Dietlinde Lau Pdf

Function Algebras on Finite Sets gives a broad introduction to the subject, leading up to the cutting edge of research. The general concepts of the Universal Algebra are given in the first part of the book, to familiarize the reader from the very beginning on with the algebraic side of function algebras. The second part covers the following topics: Galois-connection between function algebras and relation algebras, completeness criterions, and clone theory.

Author : Andrew Browder
Publisher : Unknown
Page : 294 pages
File Size : 52,9 Mb
Release : 1969
Category : Algebraic functions
ISBN : UOM:39015015691762

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Introduction to Function Algebras by Andrew Browder Pdf

Author : I. Suciu
Publisher : Springer
Page : 290 pages
File Size : 49,5 Mb
Release : 1975-06-24
Category : Mathematics
ISBN : UCAL:B4406547

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Function Algebras by I. Suciu Pdf

Under the title of Function Algebras we may now include a very large number of works. published mainly in the last decade, which consti tute one of the important chapters of functional analysis. This chapter has grown up from various problems. permanently furnished to mathe matics. by the theory of functions. using modern methods of algebra, topology and functional analysis and presenting large possibilities of applications in operators theory. Herefrom proceeds its living character, the variety of obtained results. the variety of forms and contexts in which these results can be found. This also explains the difficulty of an exhaustive exposition of these problems. The purpose of the monograph is to present a coherent exposition of the fundamental results of this theory with an orientation to their applicability to the theory of operator representations of function alge bras. The idea of such a work appeared during the seminaries on function algebras held at the Mathematical Institute in Bucharest. under the direc tion of C. Foia~ and at the Faculty of Mathematics and Mechanics under the direction of N. Boboc. It is a pleasure for the author to express his gratitude to C. Foia~ for assistance in his efforts. in general. and for the large contribution the discussions and cooperation with him had brought in the elaboration of this monograph. I also would like to thank N. Boboc for the clear discussions we have had during the seminaries and the elaboration of some chapters.

Author : S.H. Kulkarni,B.V. Limaye
Publisher : CRC Press
Page : 204 pages
File Size : 53,7 Mb
Release : 2020-08-27
Category : Mathematics
ISBN : 9781000148848

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Real Function Algebras by S.H. Kulkarni,B.V. Limaye Pdf

This self-contained reference/text presents a thorough account of the theory of real function algebras. Employing the intrinsic approach, avoiding the complexification technique, and generalizing the theory of complex function algebras, this single-source volume includes: an introduction to real Banach algebras; various generalizations of the Stone-Weierstrass theorem; Gleason parts; Choquet and Shilov boundaries; isometries of real function algebras; extensive references; and a detailed bibliography.;Real Function Algebras offers results of independent interest such as: topological conditions for the commutativity of a real or complex Banach algebra; Ransford's short elementary proof of the Bishop-Stone-Weierstrass theorem; the implication of the analyticity or antianalyticity of f from the harmonicity of Re f, Re f(2), Re f(3), and Re f(4); and the positivity of the real part of a linear functional on a subspace of C(X).;With over 600 display equations, this reference is for mathematical analysts; pure, applied, and industrial mathematicians; and theoretical physicists; and a text for courses in Banach algebras and function algebras.

Author : Arne Dür
Publisher : Springer
Page : 145 pages
File Size : 44,8 Mb
Release : 2006-11-14
Category : Mathematics
ISBN : 9783540398189

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Möbius Functions, Incidence Algebras and Power Series Representations by Arne Dür Pdf

Author : Kalle Kaarli,Alden F. Pixley
Publisher : CRC Press
Page : 378 pages
File Size : 48,6 Mb
Release : 2000-07-21
Category : Mathematics
ISBN : 1584882034

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Polynomial Completeness in Algebraic Systems by Kalle Kaarli,Alden F. Pixley Pdf

Boolean algebras have historically played a special role in the development of the theory of general or "universal" algebraic systems, providing important links between algebra and analysis, set theory, mathematical logic, and computer science. It is not surprising then that focusing on specific properties of Boolean algebras has lead to new directions in universal algebra. In the first unified study of polynomial completeness, Polynomial Completeness in Algebraic Systems focuses on and systematically extends another specific property of Boolean algebras: the property of affine completeness. The authors present full proof that all affine complete varieties are congruence distributive and that they are finitely generated if and only if they can be presented using only a finite number of basic operations. In addition to these important findings, the authors describe the different relationships between the properties of lattices of equivalence relations and the systems of functions compatible with them. An introductory chapter surveys the appropriate background material, exercises in each chapter allow readers to test their understanding, and open problems offer new research possibilities. Thus Polynomial Completeness in Algebraic Systems constitutes an accessible, coherent presentation of this rich topic valuable to both researchers and graduate students in general algebraic systems.

Author : Jorge Almeida
Publisher : World Scientific
Page : 532 pages
File Size : 45,8 Mb
Release : 1995-01-27
Category : Mathematics
ISBN : 9789814501569

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Finite Semigroups and Universal Algebra by Jorge Almeida Pdf

Motivated by applications in theoretical computer science, the theory of finite semigroups has emerged in recent years as an autonomous area of mathematics. It fruitfully combines methods, ideas and constructions from algebra, combinatorics, logic and topology. In simple terms, the theory aims at a classification of finite semigroups in certain classes called “pseudovarieties”. The classifying characteristics have both structural and syntactical aspects, the general connection between them being part of universal algebra. Besides providing a foundational study of the theory in the setting of arbitrary abstract finite algebras, this book stresses the syntactical approach to finite semigroups. This involves studying (relatively) free and profinite free semigroups and their presentations. The techniques used are illustrated in a systematic study of various operators on pseudovarieties of semigroups. Contents:Finite Universal Algebra:Elements of Universal AlgebraOrder and TopologyFinite AlgebrasDecidabilityFinite Semigroups and Monoids:PreliminariesPermutativityOperators Relating Semigroups and MonoidsSemigroups Whose Regular D-Classes are SubsemigroupsThe JoinThe Semidirect ProductThe PowerFactorization of Implicit OperationsOpen Problems Readership: Mathematicians and computer scientists. keywords:Inite Semigroups;Finite Monoids;Universal Algebra;Recognizable Languages;Pseudovarieties;Pseudoidentities;Implicit Operations;Relatively Free Profinite Semigroups;Semidirect Products;Power Semigroups “This book is devoted to an exciting new field where author has made important contributions, and thus it is a most welcome addition to the existing literature. It will find its place on the bookshelves of many a specialist in semigroups, as well as species of algebraists and computer scientists, including graduate students.” Semigroup Forum “The book … constitutes an important contribution to the most active part of the present theory of finite semigroups. All overwhelming majority of the results included in it is very new and has been scattered over journals so far. The book does not cover all of the theory of semigroup … but it is extremely rich in material and ideas presented with skill and dedication. The book has already influenced the area essentially, and its influence will certainly grow … I think the book is a must for researchers in the area but it is also very useful for all those who want to trace modern developments in the theory of semigroups.” Mathematics Abstracts

Author : Frank T. Birtel
Publisher : Unknown
Page : 376 pages
File Size : 50,8 Mb
Release : 1966
Category : Function algebras
ISBN : UOM:39015000971690

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Function Algebras by Frank T. Birtel Pdf

These Proceedings contain articles based on the invited addresses, submitted abstracts, and informal discussions at the International Symposium on Function Algebras held at Tulane University during April 19-24, 1965, under the joint sponsorship of the National Science Foundation (Contract No. GP-3438) and the Office of Naval Research (Contract No. NRO43-326). Research problems which appear in the Appendix were formulated and discussed on the final day of the Symposium. The term Function Algebras appearing in the title is used in its general, not its technical sense. Perhaps the more generic usage, Algebras of Functions, is advisable, but it seems pedantic to insist upon this fine semantic distinction. Thus the reader is cautioned. Within a given article, Function Algebra frequently means sup norm algebra or uniform algebra: a uniformly closed separating subalgebra of the continuous complex valued functions with 1 on a compact Hausdorff space. In titles the term is frequently used to indicate any algebra which consists of functions.

Author : B. Csákány,Ivo G. Rosenberg
Publisher : North Holland
Page : 888 pages
File Size : 49,5 Mb
Release : 1981
Category : Mathematics
ISBN : UOM:39015037748301

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Finite Algebra and Multiple-valued Logic by B. Csákány,Ivo G. Rosenberg Pdf

Author : Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor
Publisher : American Mathematical Society
Page : 496 pages
File Size : 52,9 Mb
Release : 2022-10-28
Category : Mathematics
ISBN : 9781470467975

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Algebras, Lattices, Varieties by Ralph S. Freese,Ralph N. McKenzie,George F. McNulty,Walter F. Taylor Pdf

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.

Author : Harold Garth Dales
Publisher : Springer Nature
Page : 452 pages
File Size : 53,7 Mb
Release : 2024-06-29
Category : Electronic
ISBN : 9783031445323

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Banach Function Algebras, Arens Regularity, and BSE Norms by Harold Garth Dales Pdf

Author : Charles E. Rickart
Publisher : Springer
Page : 262 pages
File Size : 40,9 Mb
Release : 1979-10-31
Category : Mathematics
ISBN : UOM:39015049296836

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Natural Function Algebras by Charles E. Rickart Pdf

The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".

Author : Charles E. Rickart
Publisher : Springer Science & Business Media
Page : 252 pages
File Size : 43,8 Mb
Release : 2012-12-06
Category : Mathematics
ISBN : 9781461380702

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Natural Function Algebras by Charles E. Rickart Pdf

The term "function algebra" usually refers to a uniformly closed algebra of complex valued continuous functions on a compact Hausdorff space. Such Banach alge bras, which are also called "uniform algebras", have been much studied during the past 15 or 20 years. Since the most important examples of uniform algebras consist of, or are built up from, analytic functions, it is not surprising that most of the work has been dominated by questions of analyticity in one form or another. In fact, the study of these special algebras and their generalizations accounts for the bulk of the re search on function algebras. We are concerned here, however, with another facet of the subject based on the observation that very general algebras of continuous func tions tend to exhibit certain properties that are strongly reminiscent of analyticity. Although there exist a variety of well-known properties of this kind that could be mentioned, in many ways the most striking is a local maximum modulus principle proved in 1960 by Hugo Rossi [RIl]. This result, one of the deepest and most elegant in the theory of function algebras, is an essential tool in the theory as we have developed it here. It holds for an arbitrary Banaeh algebra of £unctions defined on the spectrum (maximal ideal space) of the algebra. These are the algebras, along with appropriate generalizations to algebras defined on noncompact spaces, that we call "natural func tion algebras".