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Categories Of Algebraic Systems
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Author :Anatolij Ivanovic Mal'cev Publisher :Springer Science & Business Media ISBN 13 :364265374X Total Pages :331 pages Book Rating :4.6/5 (426 download)
Book Synopsis Algebraic Systems by : Anatolij Ivanovic Mal'cev
Download or read book Algebraic Systems written by Anatolij Ivanovic Mal'cev and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 331 pages. Available in PDF, EPUB and Kindle. Book excerpt: As far back as the 1920's, algebra had been accepted as the science studying the properties of sets on which there is defined a particular system of operations. However up until the forties the overwhelming majority of algebraists were investigating merely a few kinds of algebraic structures. These were primarily groups, rings and lattices. The first general theoretical work dealing with arbitrary sets with arbitrary operations is due to G. Birkhoff (1935). During these same years, A. Tarski published an important paper in which he formulated the basic prin ciples of a theory of sets equipped with a system of relations. Such sets are now called models. In contrast to algebra, model theory made abun dant use of the apparatus of mathematical logic. The possibility of making fruitful use of logic not only to study universal algebras but also the more classical parts of algebra such as group theory was dis covered by the author in 1936. During the next twenty-five years, it gradually became clear that the theory of universal algebras and model theory are very intimately related despite a certain difference in the nature of their problems. And it is therefore meaningful to speak of a single theory of algebraic systems dealing with sets on which there is defined a series of operations and relations (algebraic systems). The formal apparatus of the theory is the language of the so-called applied predicate calculus. Thus the theory can be considered to border on logic and algebra.
Book Synopsis Categories of Algebraic Systems by : M. Petrich
Download or read book Categories of Algebraic Systems written by M. Petrich and published by Springer. This book was released on 2006-11-14 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leitmotiv of this monograph is the unity of the modest part of mathematics encompassed by the algebraic and geometric structures mentioned in its title. Some of the relationships discussed here are very old, indeed "classical", some of them are quite recent, and still lack "status", but the categorical setting in which they are presented is considered here for the first time.
Book Synopsis Categories of Algebraic Systems by : M. Petrich
Download or read book Categories of Algebraic Systems written by M. Petrich and published by . This book was released on 2014-01-15 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Categories of Algebraic Systems by : M. Petrich
Download or read book Categories of Algebraic Systems written by M. Petrich and published by Lecture Notes in Mathematics. This book was released on 1976-12 with total page 232 pages. Available in PDF, EPUB and Kindle. Book excerpt: The leitmotiv of this monograph is the unity of the modest part of mathematics encompassed by the algebraic and geometric structures mentioned in its title. Some of the relationships discussed here are very old, indeed "classical", some of them are quite recent, and still lack "status", but the categorical setting in which they are presented is considered here for the first time.
Book Synopsis Categories for Types by : Roy L. Crole
Download or read book Categories for Types written by Roy L. Crole and published by Cambridge University Press. This book was released on 1993 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook explains the basic principles of categorical type theory and the techniques used to derive categorical semantics for specific type theories. It introduces the reader to ordered set theory, lattices and domains, and this material provides plenty of examples for an introduction to category theory, which covers categories, functors, natural transformations, the Yoneda lemma, cartesian closed categories, limits, adjunctions and indexed categories. Four kinds of formal system are considered in detail, namely algebraic, functional, polymorphic functional, and higher order polymorphic functional type theory. For each of these the categorical semantics are derived and results about the type systems are proved categorically. Issues of soundness and completeness are also considered. Aimed at advanced undergraduates and beginning graduates, this book will be of interest to theoretical computer scientists, logicians and mathematicians specializing in category theory.
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
Book Synopsis Partially Ordered Algebraic Systems by : Laszlo Fuchs
Download or read book Partially Ordered Algebraic Systems written by Laszlo Fuchs and published by Courier Corporation. This book was released on 2014-03-05 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph by a distinguished mathematician constitutes the first systematic summary of research concerning partially ordered groups, semigroups, rings, and fields. The high-level, self-contained treatment features numerous problems. 1963 edition.
Book Synopsis The Metamathematics of Algebraic Systems by : Lev D. Beklemishev
Download or read book The Metamathematics of Algebraic Systems written by Lev D. Beklemishev and published by Elsevier. This book was released on 2000-04-01 with total page 513 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Metamathematics of Algebraic Systems
Book Synopsis A Book of Abstract Algebra by : Charles C Pinter
Download or read book A Book of Abstract Algebra written by Charles C Pinter and published by Courier Corporation. This book was released on 2010-01-14 with total page 402 pages. Available in PDF, EPUB and Kindle. Book excerpt: Accessible but rigorous, this outstanding text encompasses all of the topics covered by a typical course in elementary abstract algebra. Its easy-to-read treatment offers an intuitive approach, featuring informal discussions followed by thematically arranged exercises. This second edition features additional exercises to improve student familiarity with applications. 1990 edition.
Book Synopsis Fundamentals of Advanced Mathematics 1 by : Henri Bourles
Download or read book Fundamentals of Advanced Mathematics 1 written by Henri Bourles and published by Elsevier. This book was released on 2017-07-10 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: This precis, comprised of three volumes, of which this book is the first, exposes the mathematical elements which make up the foundations of a number of contemporary scientific methods: modern theory on systems, physics and engineering. This first volume focuses primarily on algebraic questions: categories and functors, groups, rings, modules and algebra. Notions are introduced in a general framework and then studied in the context of commutative and homological algebra; their application in algebraic topology and geometry is therefore developed. These notions play an essential role in algebraic analysis (analytico-algebraic systems theory of ordinary or partial linear differential equations). The book concludes with a study of modules over the main types of rings, the rational canonical form of matrices, the (commutative) theory of elemental divisors and their application in systems of linear differential equations with constant coefficients. - Part of the New Mathematical Methods, Systems, and Applications series - Presents the notions, results, and proofs necessary to understand and master the various topics - Provides a unified notation, making the task easier for the reader. - Includes several summaries of mathematics for engineers
Book Synopsis The Theory of Classes of Groups by : Guo Wenbin
Download or read book The Theory of Classes of Groups written by Guo Wenbin and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 270 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the characteristics of modern algebra is the development of new tools and concepts for exploring classes of algebraic systems, whereas the research on individual algebraic systems (e. g. , groups, rings, Lie algebras, etc. ) continues along traditional lines. The early work on classes of alge bras was concerned with showing that one class X of algebraic systems is actually contained in another class F. Modern research into the theory of classes was initiated in the 1930's by Birkhoff's work [1] on general varieties of algebras, and Neumann's work [1] on varieties of groups. A. I. Mal'cev made fundamental contributions to this modern development. ln his re ports [1, 3] of 1963 and 1966 to The Fourth All-Union Mathematics Con ference and to another international mathematics congress, striking the ories of classes of algebraic systems were presented. These were later included in his book [5]. International interest in the theory of formations of finite groups was aroused, and rapidly heated up, during this time, thanks to the work of Gaschiitz [8] in 1963, and the work of Carter and Hawkes [1] in 1967. The major topics considered were saturated formations, Fitting classes, and Schunck classes. A class of groups is called a formation if it is closed with respect to homomorphic images and subdirect products. A formation is called saturated provided that G E F whenever Gjip(G) E F.
Book Synopsis Introduction to Applied Algebraic Systems by : Norman R Reilly
Download or read book Introduction to Applied Algebraic Systems written by Norman R Reilly and published by Oxford University Press. This book was released on 2009-11-02 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: This upper-level undergraduate textbook provides a modern view of algebra with an eye to new applications that have arisen in recent years. A rigorous introduction to basic number theory, rings, fields, polynomial theory, groups, algebraic geometry and elliptic curves prepares students for exploring their practical applications related to storing, securing, retrieving and communicating information in the electronic world. It will serve as a textbook for an undergraduate course in algebra with a strong emphasis on applications. The book offers a brief introduction to elementary number theory as well as a fairly complete discussion of major algebraic systems (such as rings, fields, and groups) with a view of their use in bar coding, public key cryptosystems, error-correcting codes, counting techniques, and elliptic key cryptography. This is the only entry level text for algebraic systems that includes an extensive introduction to elliptic curves, a topic that has leaped to prominence due to its importance in the solution of Fermats Last Theorem and its incorporation into the rapidly expanding applications of elliptic curve cryptography in smart cards. Computer science students will appreciate the strong emphasis on the theory of polynomials, algebraic geometry and Groebner bases. The combination of a rigorous introduction to abstract algebra with a thorough coverage of its applications makes this book truly unique.
Book Synopsis Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods by : Alexander Martsinkovsky
Download or read book Functor Categories, Model Theory, Algebraic Analysis and Constructive Methods written by Alexander Martsinkovsky and published by Springer Nature. This book was released on with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Categories of Algebraic Systems by : Jonathan D. H. Smith
Download or read book Categories of Algebraic Systems written by Jonathan D. H. Smith and published by . This book was released on 1976 with total page 217 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Non-linear Algebra by : Valeri? Valer?evich Dolotin
Download or read book Introduction to Non-linear Algebra written by Valeri? Valer?evich Dolotin and published by World Scientific. This book was released on 2007 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: Literaturverz. S. 267 - 269
Book Synopsis Introduction to Algebra by : R. Kochendorffer
Download or read book Introduction to Algebra written by R. Kochendorffer and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is intended as a textbook for an undergraduate course on algebra. In most universities a detailed study ·of abstract algebraic systems commences in the second year. By this time the student has gained some experience in mathematical reasoning so that a too elementary book would rob him of the joy and the stimulus of using his ability. I tried to make allowance for this when I chose t4e level of presentation. On the other hand, I hope that I also avoided discouraging the reader by demands which are beyond his strength. So, the first chapters will certainly not require more mathematical maturity than can reasonably be expected after the first year at the university. Apart from one exception the formal prerequisites do not exceed the syllabus of an average high school. As to the exception, I assume that the reader is familiar with the rudiments of linear algebra, i. e. addition and multiplication of matrices and the main properties of determinants. In view of the readers for whom the book is designed I felt entitled to this assumption. In the first chapters, matrices will almost exclusively occur in examples and exercises providing non-trivial instances in the theory of groups and rings. In Chapters 9 and 10 only, vector spaces and their properties will form a relevant part of the text. A reader who is not familiar with these concepts will have no difficulties in acquiring these prerequisites by any elementary textbook, e. g. [10].
Book Synopsis Applied Discrete Structures by : Ken Levasseur
Download or read book Applied Discrete Structures written by Ken Levasseur and published by Lulu.com. This book was released on 2012-02-25 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: Applied Discrete Structures, is a two semester undergraduate text in discrete mathematics, focusing on the structural properties of mathematical objects. These include matrices, functions, graphs, trees, lattices and algebraic structures. The algebraic structures that are discussed are monoids, groups, rings, fields and vector spaces. Website: http: //discretemath.org Applied Discrete Structures has been approved by the American Institute of Mathematics as part of their Open Textbook Initiative. For more information on open textbooks, visit http: //www.aimath.org/textbooks/. This version was created using Mathbook XML (https: //mathbook.pugetsound.edu/) Al Doerr is Emeritus Professor of Mathematical Sciences at UMass Lowell. His interests include abstract algebra and discrete mathematics. Ken Levasseur is a Professor of Mathematical Sciences at UMass Lowell. His interests include discrete mathematics and abstract algebra, and their implementation using computer algebra systems.
