Algebraic Theories

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Algebraic Theories

Author : E.G. Manes
Publisher : Springer Science & Business Media
ISBN 13 : 1461298601
Total Pages : 364 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Algebraic Theories by : E.G. Manes

Download or read book Algebraic Theories written by E.G. Manes and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: In the past decade, category theory has widened its scope and now inter acts with many areas of mathematics. This book develops some of the interactions between universal algebra and category theory as well as some of the resulting applications. We begin with an exposition of equationally defineable classes from the point of view of "algebraic theories," but without the use of category theory. This serves to motivate the general treatment of algebraic theories in a category, which is the central concern of the book. (No category theory is presumed; rather, an independent treatment is provided by the second chap ter.) Applications abound throughout the text and exercises and in the final chapter in which we pursue problems originating in topological dynamics and in automata theory. This book is a natural outgrowth of the ideas of a small group of mathe maticians, many of whom were in residence at the Forschungsinstitut für Mathematik of the Eidgenössische Technische Hochschule in Zürich, Switzerland during the academic year 1966-67. It was in this stimulating atmosphere that the author wrote his doctoral dissertation. The "Zürich School," then, was Michael Barr, Jon Beck, John Gray, Bill Lawvere, Fred Linton, and Myles Tierney (who were there) and (at least) Harry Appelgate, Sammy Eilenberg, John Isbell, and Saunders Mac Lane (whose spiritual presence was tangible.) I am grateful to the National Science Foundation who provided support, under grants GJ 35759 and OCR 72-03733 A01, while I wrote this book.

Algebraic Theories

Author : Leonard Dickson
Publisher : Courier Corporation
ISBN 13 : 048615520X
Total Pages : 241 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Algebraic Theories by : Leonard Dickson

Download or read book Algebraic Theories written by Leonard Dickson and published by Courier Corporation. This book was released on 2014-03-05 with total page 241 pages. Available in PDF, EPUB and Kindle. Book excerpt: This in-depth introduction to classical topics in higher algebra provides rigorous, detailed proofs for its explorations of some of mathematics' most significant concepts, including matrices, invariants, and groups. Algebraic Theories studies all of the important theories; its extensive offerings range from the foundations of higher algebra and the Galois theory of algebraic equations to finite linear groups (including Klein's "icosahedron" and the theory of equations of the fifth degree) and algebraic invariants. The full treatment includes matrices, linear transformations, elementary divisors and invariant factors, and quadratic, bilinear, and Hermitian forms, both singly and in pairs. The results are classical, with due attention to issues of rationality. Elementary divisors and invariant factors receive simple, natural introductions in connection with the classical form and a rational, canonical form of linear transformations. All topics are developed with a remarkable lucidity and discussed in close connection with their most frequent mathematical applications.

Algebraic Theories

Author : J. Adámek
Publisher : Cambridge University Press
ISBN 13 : 9780521119221
Total Pages : 268 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis Algebraic Theories by : J. Adámek

Download or read book Algebraic Theories written by J. Adámek and published by Cambridge University Press. This book was released on 2010-11-18 with total page 268 pages. Available in PDF, EPUB and Kindle. Book excerpt: Algebraic theories, introduced as a concept in the 1960s, have been a fundamental step towards a categorical view of general algebra. Moreover, they have proved very useful in various areas of mathematics and computer science. This carefully developed book gives a systematic introduction to algebra based on algebraic theories that is accessible to both graduate students and researchers. It will facilitate interactions of general algebra, category theory and computer science. A central concept is that of sifted colimits - that is, those commuting with finite products in sets. The authors prove the duality between algebraic categories and algebraic theories and discuss Morita equivalence between algebraic theories. They also pay special attention to one-sorted algebraic theories and the corresponding concrete algebraic categories over sets, and to S-sorted algebraic theories, which are important in program semantics. The final chapter is devoted to finitary localizations of algebraic categories, a recent research area.

Algebraic Equations

Author : Edgar Dehn
Publisher : Courier Corporation
ISBN 13 : 0486155102
Total Pages : 225 pages
Book Rating : 4.4/5 (861 download)

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Book Synopsis Algebraic Equations by : Edgar Dehn

Download or read book Algebraic Equations written by Edgar Dehn and published by Courier Corporation. This book was released on 2012-09-05 with total page 225 pages. Available in PDF, EPUB and Kindle. Book excerpt: Focusing on basics of algebraic theory, this text presents detailed explanations of integral functions, permutations, and groups as well as Lagrange and Galois theory. Many numerical examples with complete solutions. 1930 edition.

Algebra and Galois Theories

Author : Régine Douady
Publisher : Springer Nature
ISBN 13 : 3030327965
Total Pages : 479 pages
Book Rating : 4.0/5 (33 download)

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Book Synopsis Algebra and Galois Theories by : Régine Douady

Download or read book Algebra and Galois Theories written by Régine Douady and published by Springer Nature. This book was released on 2020-07-13 with total page 479 pages. Available in PDF, EPUB and Kindle. Book excerpt: Galois theory has such close analogies with the theory of coverings that algebraists use a geometric language to speak of field extensions, while topologists speak of "Galois coverings". This book endeavors to develop these theories in a parallel way, starting with that of coverings, which better allows the reader to make images. The authors chose a plan that emphasizes this parallelism. The intention is to allow to transfer to the algebraic framework of Galois theory the geometric intuition that one can have in the context of coverings. This book is aimed at graduate students and mathematicians curious about a non-exclusively algebraic view of Galois theory.

Introduction To Algebraic Theories

Author : Adrian Albert A
Publisher : Legare Street Press
ISBN 13 : 9781018171746
Total Pages : 0 pages
Book Rating : 4.1/5 (717 download)

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Book Synopsis Introduction To Algebraic Theories by : Adrian Albert A

Download or read book Introduction To Algebraic Theories written by Adrian Albert A and published by Legare Street Press. This book was released on 2022-10-27 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has been selected by scholars as being culturally important, and is part of the knowledge base of civilization as we know it. This work is in the "public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.

Process Algebra: Equational Theories of Communicating Processes

Author : J. C. M. Baeten
Publisher : Cambridge University Press
ISBN 13 : 0521820499
Total Pages : 477 pages
Book Rating : 4.5/5 (218 download)

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Book Synopsis Process Algebra: Equational Theories of Communicating Processes by : J. C. M. Baeten

Download or read book Process Algebra: Equational Theories of Communicating Processes written by J. C. M. Baeten and published by Cambridge University Press. This book was released on 2010 with total page 477 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents a unified overview of the various process algebras currently in use and sets the standard for the field.

Modern Algebraic Theories

Author : Leonard Eugene Dickson
Publisher :
ISBN 13 :
Total Pages : 298 pages
Book Rating : 4.:/5 (4 download)

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Book Synopsis Modern Algebraic Theories by : Leonard Eugene Dickson

Download or read book Modern Algebraic Theories written by Leonard Eugene Dickson and published by . This book was released on 1930 with total page 298 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Categorical Foundations

Author : Maria Cristina Pedicchio
Publisher : Cambridge University Press
ISBN 13 : 9780521834148
Total Pages : 452 pages
Book Rating : 4.8/5 (341 download)

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Book Synopsis Categorical Foundations by : Maria Cristina Pedicchio

Download or read book Categorical Foundations written by Maria Cristina Pedicchio and published by Cambridge University Press. This book was released on 2004 with total page 452 pages. Available in PDF, EPUB and Kindle. Book excerpt: Publisher Description

Algebraic Theory of Automata Networks

Author : Pal Domosi
Publisher : SIAM
ISBN 13 : 9780898718492
Total Pages : 270 pages
Book Rating : 4.7/5 (184 download)

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Book Synopsis Algebraic Theory of Automata Networks by : Pal Domosi

Download or read book Algebraic Theory of Automata Networks written by Pal Domosi and published by SIAM. This book was released on 2005-01-01 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: Investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories, such as those of semigroups, groups, rings, and fields. The authors also investigate automata networks as products of automata, that is, as compositions of automata obtained by cascading without feedback or with feedback of various restricted types or, most generally, with the feedback dependencies controlled by an arbitrary directed graph. They survey and extend the fundamental results in regard to automata networks, including the main decomposition theorems of Letichevsky, of Krohn and Rhodes, and of others.

Quantum Logic in Algebraic Approach

Author : Miklós Rédei
Publisher : Springer Science & Business Media
ISBN 13 : 9401590265
Total Pages : 244 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Quantum Logic in Algebraic Approach by : Miklós Rédei

Download or read book Quantum Logic in Algebraic Approach written by Miklós Rédei and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 244 pages. Available in PDF, EPUB and Kindle. Book excerpt: This work has grown out of the lecture notes that were prepared for a series of seminars on some selected topics in quantum logic. The seminars were delivered during the first semester of the 1993/1994 academic year in the Unit for Foundations of Science of the Department of History and Foundations of Mathematics and Science, Faculty of Physics, Utrecht University, The Netherlands, while I was staying in that Unit on a European Community Research Grant, and in the Center for Philosophy of Science, University of Pittsburgh, U. S. A. , where I was staying during the 1994/1995 academic year as a Visiting Fellow on a Fulbright Research Grant, and where I also was supported by the Istvan Szechenyi Scholarship Foundation. The financial support provided by these foundations, by the Center for Philosophy of Science and by the European Community is greatly acknowledged, and I wish to thank D. Dieks, the professor of the Foundations Group in Utrecht and G. Massey, the director of the Center for Philosophy of Science in Pittsburgh for making my stay at the respective institutions possible. I also wish to thank both the members of the Foundations Group in Utrecht, especially D. Dieks, C. Lutz, F. Muller, J. Uffink and P. Vermaas and the participants in the seminars at the Center for Philosophy of Science in Pittsburgh, especially N. Belnap, J. Earman, A. Janis, J. Norton, and J.

Yang-Mills Theories in Algebraic Non-covariant Gauges

Author : A. Bassetto
Publisher : World Scientific
ISBN 13 : 9789810205782
Total Pages : 254 pages
Book Rating : 4.2/5 (57 download)

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Book Synopsis Yang-Mills Theories in Algebraic Non-covariant Gauges by : A. Bassetto

Download or read book Yang-Mills Theories in Algebraic Non-covariant Gauges written by A. Bassetto and published by World Scientific. This book was released on 1991 with total page 254 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume deals with canonical quantization, Feynman rules and renormalization of Yang-Mills theories in algebraic non-covariant gauges (typically axial and light-cone gauges). The material is self-contained and presented in a basic manner according to a personal style representative of a long lasting activity in the field. Emphasis is always placed on the underlying basic concepts of Quantum Field Theory, even when particular examples are treated, details and the related difficulties are thoroughly discussed. The value of the book goes beyond the specificity of its subject.

Spectral Theory and Quantum Mechanics

Author : Valter Moretti
Publisher : Springer
ISBN 13 : 331970706X
Total Pages : 962 pages
Book Rating : 4.3/5 (197 download)

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Book Synopsis Spectral Theory and Quantum Mechanics by : Valter Moretti

Download or read book Spectral Theory and Quantum Mechanics written by Valter Moretti and published by Springer. This book was released on 2018-01-30 with total page 962 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book discusses the mathematical foundations of quantum theories. It offers an introductory text on linear functional analysis with a focus on Hilbert spaces, highlighting the spectral theory features that are relevant in physics. After exploring physical phenomenology, it then turns its attention to the formal and logical aspects of the theory. Further, this Second Edition collects in one volume a number of useful rigorous results on the mathematical structure of quantum mechanics focusing in particular on von Neumann algebras, Superselection rules, the various notions of Quantum Symmetry and Symmetry Groups, and including a number of fundamental results on the algebraic formulation of quantum theories. Intended for Master's and PhD students, both in physics and mathematics, the material is designed to be self-contained: it includes a summary of point-set topology and abstract measure theory, together with an appendix on differential geometry. The book also benefits established researchers by organizing and presenting the profusion of advanced material disseminated in the literature. Most chapters are accompanied by exercises, many of which are solved explicitly."

Clifford Algebra to Geometric Calculus

Author : David Hestenes
Publisher : Springer Science & Business Media
ISBN 13 : 9789027725615
Total Pages : 340 pages
Book Rating : 4.7/5 (256 download)

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Book Synopsis Clifford Algebra to Geometric Calculus by : David Hestenes

Download or read book Clifford Algebra to Geometric Calculus written by David Hestenes and published by Springer Science & Business Media. This book was released on 1984 with total page 340 pages. Available in PDF, EPUB and Kindle. Book excerpt: Matrix algebra has been called "the arithmetic of higher mathematics" [Be]. We think the basis for a better arithmetic has long been available, but its versatility has hardly been appreciated, and it has not yet been integrated into the mainstream of mathematics. We refer to the system commonly called 'Clifford Algebra', though we prefer the name 'Geometric Algebra' suggested by Clifford himself. Many distinct algebraic systems have been adapted or developed to express geometric relations and describe geometric structures. Especially notable are those algebras which have been used for this purpose in physics, in particular, the system of complex numbers, the quaternions, matrix algebra, vector, tensor and spinor algebras and the algebra of differential forms. Each of these geometric algebras has some significant advantage over the others in certain applications, so no one of them provides an adequate algebraic structure for all purposes of geometry and physics. At the same time, the algebras overlap considerably, so they provide several different mathematical representations for individual geometrical or physical ideas.

Fundamental Algebraic Geometry

Author : Barbara Fantechi
Publisher : American Mathematical Soc.
ISBN 13 : 0821842455
Total Pages : 354 pages
Book Rating : 4.8/5 (218 download)

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Book Synopsis Fundamental Algebraic Geometry by : Barbara Fantechi

Download or read book Fundamental Algebraic Geometry written by Barbara Fantechi and published by American Mathematical Soc.. This book was released on 2005 with total page 354 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an outline of Alexander Grothendieck's theories. This book discusses four main themes - descent theory, Hilbert and Quot schemes, the formal existence theorem, and the Picard scheme. It is suitable for those working in algebraic geometry.

Topics in Cohomological Studies of Algebraic Varieties

Author : Piotr Pragacz
Publisher : Springer Science & Business Media
ISBN 13 : 3764373423
Total Pages : 321 pages
Book Rating : 4.7/5 (643 download)

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Book Synopsis Topics in Cohomological Studies of Algebraic Varieties by : Piotr Pragacz

Download or read book Topics in Cohomological Studies of Algebraic Varieties written by Piotr Pragacz and published by Springer Science & Business Media. This book was released on 2006-03-30 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: The articles in this volume study various cohomological aspects of algebraic varieties: - characteristic classes of singular varieties; - geometry of flag varieties; - cohomological computations for homogeneous spaces; - K-theory of algebraic varieties; - quantum cohomology and Gromov-Witten theory. The main purpose is to give comprehensive introductions to the above topics through a series of "friendly" texts starting from a very elementary level and ending with the discussion of current research. In the articles, the reader will find classical results and methods as well as new ones. Numerous examples will help to understand the mysteries of the cohomological theories presented. The book will be a useful guide to research in the above-mentioned areas. It is adressed to researchers and graduate students in algebraic geometry, algebraic topology, and singularity theory, as well as to mathematicians interested in homogeneous varieties and symmetric functions. Most of the material exposed in the volume has not appeared in books before. Contributors: Paolo Aluffi Michel Brion Anders Skovsted Buch Haibao Duan Ali Ulas Ozgur Kisisel Piotr Pragacz Jörg Schürmann Marek Szyjewski Harry Tamvakis

Fundamental Structures of Algebra and Discrete Mathematics

Author : Stephan Foldes
Publisher : John Wiley & Sons
ISBN 13 : 1118031431
Total Pages : 362 pages
Book Rating : 4.1/5 (18 download)

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Book Synopsis Fundamental Structures of Algebra and Discrete Mathematics by : Stephan Foldes

Download or read book Fundamental Structures of Algebra and Discrete Mathematics written by Stephan Foldes and published by John Wiley & Sons. This book was released on 2011-02-14 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: Introduces and clarifies the basic theories of 12 structural concepts, offering a fundamental theory of groups, rings and other algebraic structures. Identifies essentials and describes interrelationships between particular theories. Selected classical theorems and results relevant to current research are proved rigorously within the theory of each structure. Throughout the text the reader is frequently prompted to perform integrated exercises of verification and to explore examples.